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Journal articles on the topic 'Packing chromatic number'

Author: Grafiati

Published: 7 July 2024

Last updated: 31 July 2025

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1

Brešar, Boštjan, Sandi Klavžar, Douglas F. Rall, and Kirsti Wash. "Packing chromatic number versus chromatic and clique number." Aequationes mathematicae 92, no. 3 (2017): 497–513. http://dx.doi.org/10.1007/s00010-017-0520-9.

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2

Durgun, Derya, and Busra Ozen-Dortok. "Packing chromatic number of transformation graphs." Thermal Science 23, Suppl. 6 (2019): 1991–95. http://dx.doi.org/10.2298/tsci190720363d.

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Graph coloring is an assignment of labels called colors to elements of a graph. The packing coloring was introduced by Goddard et al. [1] in 2008 which is a kind of coloring of a graph. This problem is NP-complete for general graphs. In this paper, we consider some transformation graphs and generalized their packing chromatic numbers.

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3

Balogh, József, Alexandr Kostochka, and Xujun Liu. "Packing chromatic number of cubic graphs." Discrete Mathematics 341, no. 2 (2018): 474–83. http://dx.doi.org/10.1016/j.disc.2017.09.014.

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4

Ekstein, Jan, Přemysl Holub, and Bernard Lidický. "Packing chromatic number of distance graphs." Discrete Applied Mathematics 160, no. 4-5 (2012): 518–24. http://dx.doi.org/10.1016/j.dam.2011.11.022.

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5

Torres, Pablo, and Mario Valencia-Pabon. "The packing chromatic number of hypercubes." Discrete Applied Mathematics 190-191 (August 2015): 127–40. http://dx.doi.org/10.1016/j.dam.2015.04.006.

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6

Ferme, Jasmina. "A characterization of 4-χρ-(vertex-)critical graphs". Filomat 36, № 19 (2022): 6481–501. http://dx.doi.org/10.2298/fil2219481f.

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Given a graph G, a function c : V(G) ?{1,..., k} with the property that for every u?v, c(u) = c(v) = i implies that the distance between u and v is greater than i, is called a k-packing coloring of G. The smallest integer k for which there exists a k-packing coloring of G is called the packing chromatic number of G, and is denoted by ??(G). Packing chromatic vertex-critical graphs are the graphs G for which ??(G ? x) < ??(G) holds for every vertex x of G. A graph G is called a packing chromatic critical graph if for every proper subgraph H of G, ??(H) < ??(G). Both of the mentioned varia

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7

William, Albert, Roy Santiago, and Indra Rajasingh. "Packing Chromatic Number of Cycle Related Graphs." International Journal of Mathematics and Soft Computing 4, no. 1 (2014): 27. http://dx.doi.org/10.26708/ijmsc.2014.1.4.04.

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8

Torres, Pablo, and Mario Valencia-Pabon. "On the packing chromatic number of hypercubes." Electronic Notes in Discrete Mathematics 44 (November 2013): 263–68. http://dx.doi.org/10.1016/j.endm.2013.10.041.

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9

Lemdani, Rachid, Moncef Abbas, and Jasmina Ferme. "Packing chromatic numbers of finite super subdivisions of graphs." Filomat 34, no. 10 (2020): 3275–86. http://dx.doi.org/10.2298/fil2010275l.

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Given a graph G and a positive integer i, an i-packing in G is a subset W of the vertex set of G such that the distance between any two distinct vertices from W is greater than i. The packing chromatic number of a graph G, ??(G), is the smallest integer k such that the vertex set of G can be partitioned into sets Vi, i ? {1,..., k}, where each Vi is an i-packing. In this paper, we present some general properties of packing chromatic numbers of finite super subdivisions of graphs. We determine the packing chromatic numbers of the finite super subdivisions of complete graphs, cycles and some nei

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10

CHALUVARAJU, B., and M. KUMARA. "The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs." Journal of Ultra Scientist of Physical Sciences Section A 33, no. 5 (2021): 66–73. http://dx.doi.org/10.22147/jusps-a/330501.

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The packing chromatic number χ_{p}(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,...,Vk , where vertices in Vi have pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes._{}

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11

Goddard, Wayne, and Honghai Xu. "The S-packing chromatic number of a graph." Discussiones Mathematicae Graph Theory 32, no. 4 (2012): 795. http://dx.doi.org/10.7151/dmgt.1642.

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12

Brešar, Boštjan, Sandi Klavžar, and Douglas F. Rall. "Packing Chromatic Number of Base-3 Sierpiński Graphs." Graphs and Combinatorics 32, no. 4 (2015): 1313–27. http://dx.doi.org/10.1007/s00373-015-1647-x.

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13

Balogh, József, Alexandr Kostochka, and Xujun Liu. "Packing Chromatic Number of Subdivisions of Cubic Graphs." Graphs and Combinatorics 35, no. 2 (2019): 513–37. http://dx.doi.org/10.1007/s00373-019-02016-3.

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14

Finbow, Arthur S., and Douglas F. Rall. "On the packing chromatic number of some lattices." Discrete Applied Mathematics 158, no. 12 (2010): 1224–28. http://dx.doi.org/10.1016/j.dam.2009.06.001.

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15

Fiala, Jiří, Sandi Klavžar, and Bernard Lidický. "The packing chromatic number of infinite product graphs." European Journal of Combinatorics 30, no. 5 (2009): 1101–13. http://dx.doi.org/10.1016/j.ejc.2008.09.014.

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16

Fresán-Figueroa, J., D. González-Moreno, and M. Olsen. "On the packing chromatic number of Moore graphs." Discrete Applied Mathematics 289 (January 2021): 185–93. http://dx.doi.org/10.1016/j.dam.2020.10.009.

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17

Gastineau, Nicolas, Hamamache Kheddouci, and Olivier Togni. "Subdivision into i-packings and S-packing chromatic number of some lattices." Ars Mathematica Contemporanea 9, no. 2 (2015): 321–44. http://dx.doi.org/10.26493/1855-3974.436.178.

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18

R, Srinivasan, and Vivekanandan M. "On Packing Colouring of Transformation of Path, Cycle and Wheel Graphs." Indian Journal of Science and Technology 14, no. 23 (2021): 1975–81. https://doi.org/10.17485/IJST/v14i23.606.

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Abstract <strong>Objectives</strong>: To compute the packing chromatic number of transformation of path graph, cycle graph and wheel graph. <strong>Methods</strong>: The packing chromatic number of  <em>Xpc (H)</em> of a graph <em>H </em>is the least integer <em>m </em> in such a way that there is a mapping C: V(H)→(1,2,…,m} such that the distance between any two nodes of colour <em>k </em>is greater than k+1. <strong>Findings</strong>:<strong> </strong>The packing chromatic number of the transformation

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19

Brešar, Boštjan, Sandi Klavžar, Douglas F. Rall, and Kirsti Wash. "Packing chromatic number under local changes in a graph." Discrete Mathematics 340, no. 5 (2017): 1110–15. http://dx.doi.org/10.1016/j.disc.2016.09.030.

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20

Gastineau, Nicolas, Přemysl Holub, and Olivier Togni. "On the packing chromatic number of subcubic outerplanar graphs." Discrete Applied Mathematics 255 (February 2019): 209–21. http://dx.doi.org/10.1016/j.dam.2018.07.034.

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21

Božović, Dragana, and Iztok Peterin. "A note on the packing chromatic number of lexicographic products." Discrete Applied Mathematics 293 (April 2021): 34–37. http://dx.doi.org/10.1016/j.dam.2021.01.010.

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22

William, Albert, S. Roy, and Indra Rajasingh. "Packing Chromatic Number of Circular Fans and Mesh of Trees." International Journal of Mathematics and Soft Computing 4, no. 2 (2014): 145. http://dx.doi.org/10.26708/ijmsc.2014.2.4.15.

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23

Korže, Danilo, and Aleksander Vesel. "On the packing chromatic number of square and hexagonal lattice." Ars Mathematica Contemporanea 7, no. 1 (2013): 13–22. http://dx.doi.org/10.26493/1855-3974.255.88d.

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24

Roy, S. "Packing chromatic number of certain fan and wheel related graphs." AKCE International Journal of Graphs and Combinatorics 14, no. 1 (2017): 63–69. http://dx.doi.org/10.1016/j.akcej.2016.11.001.

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25

Kristiana, Arika Indah, Sri Moeliyana Citra, Dafik, Ridho Alfarisi, and Robiatul Adawiyah. "On The Packing k-Coloring of Some Family Trees." Statistics, Optimization & Information Computing 13, no. 3 (2024): 1291–98. https://doi.org/10.19139/soic-2310-5070-2047.

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All graphs in this paper are simple and connected. Let $G=(V,E)$ be a graph where $V(G)$ is nonempty of vertex set of $G$ and $E(G)$ is possibly empty set of unordered pairs of elements of $V(G)$. The distance from $u$ to $v$ in $G$ is the length of a shortest path joining them, denoted by $d(u,v)$. For some positive integer $k$, a function $ c:V(G)\rightarrow \{1,2,...k\} $ is called packing $k-$coloring if any two not adjacent vertices $u$ and $v$, $c(u)=c(v)=i$ and $d(u,v)\geq i+1$. The minimum number $k$ such that the graph $G$ has a packing $k-$coloring is called the packing chromatic num

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26

Urenda, Alje Marie M., Jacel Angeline V. Lingcong, Normina A. Batucan, Joel G. Adanza, and Michael P. Baldado Jr. "Packing chromatic number of the join of some classes of graphs." International Mathematical Forum 17, no. 2 (2022): 75–87. http://dx.doi.org/10.12988/imf.2022.912315.

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27

Brešar, Boštjan, and Jasmina Ferme. "An infinite family of subcubic graphs with unbounded packing chromatic number." Discrete Mathematics 341, no. 8 (2018): 2337–42. http://dx.doi.org/10.1016/j.disc.2018.05.004.

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28

Bidine, Ez-Zobair, Taoufiq Gadi, and Mustapha Kchikech. "The exponential growth of the packing chromatic number of iterated Mycielskians." Discrete Applied Mathematics 341 (December 2023): 232–41. http://dx.doi.org/10.1016/j.dam.2023.08.007.

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29

Ferme, Jasmina, and Dasa Stesl. "On distance dominator packing coloring in graphs." Filomat 35, no. 12 (2021): 4005–16. http://dx.doi.org/10.2298/fil2112005f.

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Let G be a graph and let S = (s1,s2,..., sk) be a non-decreasing sequence of positive integers. An S-packing coloring of G is a mapping c : V(G) ? {1, 2,..., k} with the following property: if c(u) = c(v) = i, then d(u,v) > si for any i ? {1, 2,...,k}. In particular, if S = (1, 2, 3, ..., k), then S-packing coloring of G is well known under the name packing coloring. Next, let r be a positive integer and u,v ? V(G). A vertex u r-distance dominates a vertex v if dG(u, v)? r. In this paper, we present a new concept of a coloring, namely distance dominator packing coloring, defined as follows.

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30

Brešar, Boštjan, Sandi Klavžar, and Douglas F. Rall. "On the packing chromatic number of Cartesian products, hexagonal lattice, and trees." Discrete Applied Mathematics 155, no. 17 (2007): 2303–11. http://dx.doi.org/10.1016/j.dam.2007.06.008.

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31

Brešar, Boštjan, Sandi Klavžar, and Douglas F. Rall. "On the packing chromatic number of Cartesian products, hexagonal lattice, and trees." Electronic Notes in Discrete Mathematics 29 (August 2007): 237–41. http://dx.doi.org/10.1016/j.endm.2007.07.040.

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32

Citra, S. M., A. I. Kristiana, R. Adawiyah, Dafik, and R. M. Prihandini. "On the packing chromatic number of vertex amalgamation of some related tree graph." Journal of Physics: Conference Series 1836, no. 1 (2021): 012025. http://dx.doi.org/10.1088/1742-6596/1836/1/012025.

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33

Rall, Douglas F., Boštjan Brešar, Arthur S. Finbow, and Sandi Klavžar. "On the Packing Chromatic Number of Trees, Cartesian Products and Some Infinite Graphs." Electronic Notes in Discrete Mathematics 30 (February 2008): 57–61. http://dx.doi.org/10.1016/j.endm.2008.01.011.

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34

Martin, Barnaby, Franco Raimondi, Taolue Chen, and Jos Martin. "The packing chromatic number of the infinite square lattice is between 13 and 15." Discrete Applied Mathematics 225 (July 2017): 136–42. http://dx.doi.org/10.1016/j.dam.2017.03.013.

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35

BUJTÁS, CSILLA, GYÖRGY DÓSA, CSANÁD IMREH, JUDIT NAGY-GYÖRGY, and ZSOLT TUZA. "THE GRAPH-BIN PACKING PROBLEM." International Journal of Foundations of Computer Science 22, no. 08 (2011): 1971–93. http://dx.doi.org/10.1142/s012905411100915x.

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We deal with a very general problem: a given graph G is to be "packed" into a host graph H, and we are asked about some natural optimization questions concerning this packing. The problem has never been investigated before in this general form. The input of the problem is a simple graph G = (V, E) with lower and upper bounds on its edges and weights on its vertices. The vertices correspond to items which have to be packed into the vertices (bins) of a host graph, such that each host vertex can accommodate at most L weight in total, and if two items are adjacent in G, then the distance of their

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36

Brešar, Boštjan, Sandi Klavžar, Douglas F. Rall, and Kirsti Wash. "Packing chromatic number, $$\mathbf (1, 1, 2, 2) $$ ( 1 , 1 , 2 , 2 ) -colorings, and characterizing the Petersen graph." Aequationes mathematicae 91, no. 1 (2017): 169–84. http://dx.doi.org/10.1007/s00010-016-0461-8.

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37

Mirdamad, Shahrzad S., and Doost Ali Mojdeh. "\(e\)-Injective Coloring: \(2\)-Distance and Injective Coloring Conjectures." Journal of Combinatorial Mathematics and Combinatorial Computing 123, no. 1 (2024): 383–96. https://doi.org/10.61091/jcmcc123-27.

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An injective coloring of a given graph \(G = (V, E)\) is a vertex coloring of \(G\) such that any two vertices with a common neighbor receive distinct colors. An \(e\)-injective coloring of a graph \(G\) is a vertex coloring of \(G\) in which any two vertices \(v, u\) with a common edge \(e\) (\(e \neq uv\)) receive distinct colors; in other words, any two end vertices of a path \(P_4\) in \(G\) achieve different colors. With this new definition, we want to take a review of injective coloring of a graph from the new point of view. For this purpose, we review the conjectures raised so far in th

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38

Bozhko, Tetiana. "Infographics as an Information System: Information Encoding Issues." Bulletin of Kyiv National University of Culture and Arts. Series in Arts, no. 46 (May 22, 2022): 198–208. https://doi.org/10.31866/2410-1176.46.2022.258795.

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The purpose of the study is to reflect the relationship between the number of information encoding tools involved in the design of infographics, and the convenience and effectiveness of perception of its content. Infographics are considered as a screen message, within which information is presented with different ways of visual coding. The variability of decoded elements and their interaction can lead to synergy and dissonance of the content components of infographics, which encourages in-depth study of the conditions for combining encoded elements into a coherent information system. The metho

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39

Fowler, Katie E., Anjali A. Mandawala, and Darren K. Griffin. "The role of chromosome segregation and nuclear organisation in human subfertility." Biochemical Society Transactions 47, no. 1 (2019): 425–32. http://dx.doi.org/10.1042/bst20180231.

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Abstract Spermatogenesis is central to successful sexual reproduction, producing large numbers of haploid motile male gametes. Throughout this process, a series of equational and reductional chromosome segregation precedes radical repackaging of the haploid genome. Faithful chromosome segregation is thus crucial, as is an ordered spatio-temporal ‘dance’ of packing a large amount of chromatin into a very small space. Ergo, when the process goes wrong, this is associated with an improper chromosome number, nuclear position and/or chromatin damage in the sperm head. Generally, screening for overa

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40

Chen, Hao. "Ball packings with high chromatic numbers from strongly regular graphs." Discrete Mathematics 340, no. 7 (2017): 1645–48. http://dx.doi.org/10.1016/j.disc.2017.03.006.

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41

Pigozzi, M. I., and A. J. Solari. "Equal frequencies of recombination nodules in both sexes of the pigeon suggest a basic difference with eutherian mammals." Genome 42, no. 2 (1999): 315–21. http://dx.doi.org/10.1139/g98-137.

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The total number of recombination nodules (RNs) in the autosomal synaptonemal complexes (SCs) is statistically equivalent in oocytes and spermatocytes from the domestic pigeon Columba livia. The distribution on RNs along the three longest autosomes is also equivalent in oocytes and spermatocytes. The numbers of RNs show a linear relationship when plotted against SC length both in oocytes and spermatocytes. On the other hand, the ZW pair shows a single and strictly localized RN near the synaptic termini, but the ZZ pair shows unrestricted location of RNs (average 3.8). The ZW and ZZ pairs of th

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42

Athey, B. D., M. F. Smith, D. A. Rankert, S. P. Williams, and J. P. Langmore. "The diameters of frozen-hydrated chromatin fibers increase with DNA linker length: evidence in support of variable diameter models for chromatin." Journal of Cell Biology 111, no. 3 (1990): 795–806. http://dx.doi.org/10.1083/jcb.111.3.795.

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The diameters of chromatin fibers from Thyone briareus (sea cucumber) sperm (DNA linker length, n = 87 bp) and Necturus maculosus (mudpuppy) erythrocytes (n = 48 bp) were investigated. Soluble fibers were frozen into vitrified aqueous solutions of physiological ionic strength (124 mM), imaged by cryo-EM, and measured interactively using quantitative computer image-processing techniques. Frozen-hydrated Thyone and Necturus fibers had significantly different mean diameters of 43.5 nm (SD = 4.2 nm; SEM = 0.61 nm) and 32.0 nm (SD = 3.0 nm; SEM = 0.36 nm), respectively. Evaluation of previously pub

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43

Widłak, Piotr. "DNA microarrays, a novel approach in studies of chromatin structure." Acta Biochimica Polonica 51, no. 1 (2004): 1–8. http://dx.doi.org/10.18388/abp.2004_3592.

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The DNA microarray technology delivers an experimental tool that allows surveying expression of genetic information on a genome-wide scale at the level of single genes--for the new field termed functional genomics. Gene expression profiling--the primary application of DNA microarrays technology--generates monumental amounts of information concerning the functioning of genes, cells and organisms. However, the expression of genetic information is regulated by a number of factors that cannot be directly targeted by standard gene expression profiling. The genetic material of eukaryotic cells is pa

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44

Brand, Cara L., and Mia T. Levine. "Functional Diversification of Chromatin on Rapid Evolutionary Timescales." Annual Review of Genetics 55, no. 1 (2021): 401–25. http://dx.doi.org/10.1146/annurev-genet-071719-020301.

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Repeat-enriched genomic regions evolve rapidly and yet support strictly conserved functions like faithful chromosome transmission and the preservation of genome integrity. The leading resolution to this paradox is that DNA repeat–packaging proteins evolve adaptively to mitigate deleterious changes in DNA repeat copy number, sequence, and organization. Exciting new research has tested this model of coevolution by engineering evolutionary mismatches between adaptively evolving chromatin proteins of one species and the DNA repeats of a close relative. Here, we review these innovative evolution-gu

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45

Selvam, Kathiresan, John J. Wyrick, and Michael A. Parra. "DNA Repair in Nucleosomes: Insights from Histone Modifications and Mutants." International Journal of Molecular Sciences 25, no. 8 (2024): 4393. http://dx.doi.org/10.3390/ijms25084393.

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DNA repair pathways play a critical role in genome stability, but in eukaryotic cells, they must operate to repair DNA lesions in the compact and tangled environment of chromatin. Previous studies have shown that the packaging of DNA into nucleosomes, which form the basic building block of chromatin, has a profound impact on DNA repair. In this review, we discuss the principles and mechanisms governing DNA repair in chromatin. We focus on the role of histone post-translational modifications (PTMs) in repair, as well as the molecular mechanisms by which histone mutants affect cellular sensitivi

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46

Nguyen, Thinh T., Joanne G. A. Savory, Travis Brooke-Bisschop, et al. "Cdx2 Regulates Gene Expression through Recruitment of Brg1-associated Switch-Sucrose Non-fermentable (SWI-SNF) Chromatin Remodeling Activity." Journal of Biological Chemistry 292, no. 8 (2017): 3389–99. http://dx.doi.org/10.1074/jbc.m116.752774.

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The packaging of genomic DNA into nucleosomes creates a barrier to transcription that can be relieved through ATP-dependent chromatin remodeling via complexes such as the switch-sucrose non-fermentable (SWI-SNF) chromatin remodeling complex. The SWI-SNF complex remodels chromatin via conformational or positional changes of nucleosomes, thereby altering the access of transcriptional machinery to target genes. The SWI-SNF complex has limited ability to bind to sequence-specific elements, and, therefore, its recruitment to target loci is believed to require interaction with DNA-associated transcr

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47

Pebernard, Stephanie, W. Hayes McDonald, Yelena Pavlova, John R. Yates, and Michael N. Boddy. "Nse1, Nse2, and a Novel Subunit of the Smc5-Smc6 Complex, Nse3, Play a Crucial Role in Meiosis." Molecular Biology of the Cell 15, no. 11 (2004): 4866–76. http://dx.doi.org/10.1091/mbc.e04-05-0436.

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The structural maintenance of chromosomes (SMC) family of proteins play key roles in the organization, packaging, and repair of chromosomes. Cohesin (Smc1+3) holds replicated sister chromatids together until mitosis, condensin (Smc2+4) acts in chromosome condensation, and Smc5+6 performs currently enigmatic roles in DNA repair and chromatin structure. The SMC heterodimers must associate with non-SMC subunits to perform their functions. Using both biochemical and genetic methods, we have isolated a novel subunit of the Smc5+6 complex, Nse3. Nse3 is an essential nuclear protein that is required

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48

Lindstrom, Kimberly C., Jay C. Vary, Mark R. Parthun, Jeffrey Delrow, and Toshio Tsukiyama. "Isw1 Functions in Parallel with the NuA4 and Swr1 Complexes in Stress-Induced Gene Repression." Molecular and Cellular Biology 26, no. 16 (2006): 6117–29. http://dx.doi.org/10.1128/mcb.00642-06.

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ABSTRACT The packaging of DNA into chromatin allows eukaryotic cells to organize and compact their genomes but also creates an environment that is generally repressive to nuclear processes that depend upon DNA accessibility. There are several classes of enzymes that modulate the primary structure of chromatin to regulate various DNA-dependent processes. The biochemical activities of the yeast Isw1 ATP-dependent chromatin-remodeling enzyme have been well characterized in vitro, but little is known about how these activities are utilized in vivo. In this work, we sought to discern genetic backgr

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49

Martins, Flavia, Ana L. Machado, Patricia D. Carvalho, et al. "Abstract A006: Chromatin remodeling as a potential epigenetic mechanism of tolerance to KRAS loss." Molecular Cancer Research 21, no. 5_Supplement (2023): A006. http://dx.doi.org/10.1158/1557-3125.ras23-a006.

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Abstract KRAS-targeted inhibition yielded promising, yet far from ideal, clinical responses, revealing that cancer cells easily bypass KRAS loss. Therefore, we aim to understand how mutant KRAS cancer cells tolerate so well the loss of a key oncogene to which they were addicted to. KRAS expression was silenced through siRNAs in colorectal cancer (CRC) cell lines that carry KRAS mutations. The proteome characterization was obtained by mass spectrometry and the expression of significantly altered proteins was validated by western blotting. Chromatin states were investigated using electron micros

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50

Jiang, Xuanzhao, Tatiana A. Soboleva, and David J. Tremethick. "Short Histone H2A Variants: Small in Stature but not in Function." Cells 9, no. 4 (2020): 867. http://dx.doi.org/10.3390/cells9040867.

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The dynamic packaging of DNA into chromatin regulates all aspects of genome function by altering the accessibility of DNA and by providing docking pads to proteins that copy, repair and express the genome. Different epigenetic-based mechanisms have been described that alter the way DNA is organised into chromatin, but one fundamental mechanism alters the biochemical composition of a nucleosome by substituting one or more of the core histones with their variant forms. Of the core histones, the largest number of histone variants belong to the H2A class. The most divergent class is the designated

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