Relevant bibliographies by topics / Packing chromatic number

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Packing chromatic number'

Author: Grafiati
Published: 7 July 2024
Last updated: 31 July 2025

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Journal articles on the topic "Packing chromatic number"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Packing chromatic number"

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Mortada, Maidoun. "The b-chromatic number of regular graphs." Thesis, Lyon 1, 2013. http://www.theses.fr/2013LYO10116.

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Les deux problèmes majeurs considérés dans cette thèse : le b-coloration problème et le graphe emballage problème. 1. Le b-coloration problème : Une coloration des sommets de G s'appelle une b-coloration si chaque classe de couleur contient au moins un sommet qui a un voisin dans toutes les autres classes de couleur. Le nombre b-chromatique b(G) de G est le plus grand entier k pour lequel G a une b-coloration avec k couleurs. EL Sahili et Kouider demandent s'il est vrai que chaque graphe d-régulier G avec le périmètre au moins 5 satisfait b(G) = d + 1. Blidia, Maffray et Zemir ont montré que l
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Tarhini, Batoul. "Oriented paths in digraphs and the S-packing coloring of subcubic graph." Electronic Thesis or Diss., Bourgogne Franche-Comté, 2023. http://www.theses.fr/2023UBFCK079.

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Cette thèse de doctorat est divisée en deux parties principales: La partie I explore l'existence de chemins orientés dans les digraphes, cherchant à établir un lien entre le nombre chromatique d'un digraphe et l'existence de chemins orientés spécifiques en tant que sous-digraphes. Les digraphes contenus dans n'importe quel digraphe n-chromatique sont appelés n-universels. Nous examinons deux conjectures : la conjecture de Burr, qui affirme que chaque arbre orienté d'ordre n est (2n-2)-universel, et la conjecture d'El Sahili, qui déclare que chaque chemin orienté d'ordre n est n-universel. Pour
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Moustrou, Philippe. "Geometric distance graphs, lattices and polytopes." Thesis, Bordeaux, 2017. http://www.theses.fr/2017BORD0802/document.

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Un graphe métrique G(X;D) est un graphe dont l’ensemble des sommets est l’ensemble X des points d’un espace métrique (X; d), et dont les arêtes relient les paires fx; yg de sommets telles que d(x; y) 2 D. Dans cette thèse, nous considérons deux problèmes qui peuvent être interprétés comme des problèmes de graphes métriques dans Rn. Premièrement, nous nous intéressons au célèbre problème d’empilements de sphères, relié au graphe métrique G(Rn; ]0; 2r[) pour un rayon de sphère r donné. Récemment, Venkatesh a amélioré d’un facteur log log n la meilleure borne inférieure connue pour un empilement
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Changiz, Rezaei Seyed Saeed. "Entropy and Graphs." Thesis, 2014. http://hdl.handle.net/10012/8173.

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The entropy of a graph is a functional depending both on the graph itself and on a probability distribution on its vertex set. This graph functional originated from the problem of source coding in information theory and was introduced by J. K\"{o}rner in 1973. Although the notion of graph entropy has its roots in information theory, it was proved to be closely related to some classical and frequently studied graph theoretic concepts. For example, it provides an equivalent definition for a graph to be perfect and it can also be applied to obtain lower bounds in graph covering problems. In
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Book chapters on the topic "Packing chromatic number"

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Subercaseaux, Bernardo, and Marijn J. H. Heule. "The Packing Chromatic Number of the Infinite Square Grid is 15." In Tools and Algorithms for the Construction and Analysis of Systems. Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30823-9_20.

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AbstractA packing k-coloring is a natural variation on the standard notion of graph k-coloring, where vertices are assigned numbers from $$\{1, \ldots , k\}$$ { 1 , … , k } , and any two vertices assigned a common color $$c \in \{1, \ldots , k\}$$ c ∈ { 1 , … , k } need to be at a distance greater than c (as opposed to 1, in standard graph colorings). Despite a sequence of incremental work, determining the packing chromatic number of the infinite square grid has remained an open problem since its introduction in 2002. We culminate the search by proving this number to be 15. We achieve this res
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Wang, Hong, and Norbert Sauer. "The Chromatic Number of the Two-Packing of a Forest." In The Mathematics of Paul Erdős II. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7254-4_12.

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Wang, Hong, and Norbert Sauer. "The Chromatic Number of the Two-packing of a Forest." In Algorithms and Combinatorics. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60406-5_11.

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Bianchi, Marco E. "|The HMG-box domain." In DNA-Protein: Structural Interactions. Oxford University PressOxford, 1995. http://dx.doi.org/10.1093/oso/9780199634545.003.0007.

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Abstract The HMG-box is a new kind of eukaryotic protein domain involved in DNA binding. It has been discovered in a number of chromatin proteins, general transcription factors, and transcriptional regulators which control tissue differentiation and sex determination. The most unusual feature of HMG-boxes is that they recognise and/ or produce primarily conformational features in DNA, even if some members of this family can also bind sequence-specifically to particular sites on linear DNA. The diverse set of HMG-box-containing proteins (which we will call ‘HMG-box proteins’ from now on) appear
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Conference papers on the topic "Packing chromatic number"

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Kühn, Daniela, and Deryk Osthus. "Critical chromatic number and the complexity of perfect packings in graphs." In the seventeenth annual ACM-SIAM symposium. ACM Press, 2006. http://dx.doi.org/10.1145/1109557.1109651.

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