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Journal articles on the topic 'Anti-Ramsey number'

Author: Grafiati

Published: 6 September 2023

Last updated: 25 May 2024

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1

Gorgol, Izolda, and Anna Lechowska. "Anti-Ramsey number of Hanoi graphs." Discussiones Mathematicae Graph Theory 39, no. 1 (2019): 285. http://dx.doi.org/10.7151/dmgt.2078.

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2

Haas, Ruth, and Michael Young. "The anti-Ramsey number of perfect matching." Discrete Mathematics 312, no. 5 (2012): 933–37. http://dx.doi.org/10.1016/j.disc.2011.10.017.

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3

Özkahya, Lale, and Michael Young. "Anti-Ramsey number of matchings in hypergraphs." Discrete Mathematics 313, no. 20 (2013): 2359–64. http://dx.doi.org/10.1016/j.disc.2013.06.015.

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4

Fang, Chunqiu, Ervin Győri, Mei Lu, and Jimeng Xiao. "On the anti-Ramsey number of forests." Discrete Applied Mathematics 291 (March 2021): 129–42. http://dx.doi.org/10.1016/j.dam.2020.08.027.

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5

余, 婷. "Anti-Ramsey Number of 4-Cycle in Complete Multipartite Graphs." Advances in Applied Mathematics 10, no. 07 (2021): 2378–84. http://dx.doi.org/10.12677/aam.2021.107249.

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6

Axenovich, Maria, Tao Jiang, and Z. Tuza. "Local Anti-Ramsey Numbers of Graphs." Combinatorics, Probability and Computing 12, no. 5-6 (2003): 495–511. http://dx.doi.org/10.1017/s0963548303005868.

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A subgraph H in an edge-colouring is properly coloured if incident edges of H are assigned different colours, and H is rainbow if no two edges of H are assigned the same colour. We study properly coloured subgraphs and rainbow subgraphs forced in edge-colourings of complete graphs in which each vertex is incident to a large number of colours.

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7

周, 韦佳. "The Anti-Ramsey Number of Trees in Maximal Out-Planar Graph." Advances in Applied Mathematics 13, no. 01 (2024): 169–75. http://dx.doi.org/10.12677/aam.2024.131020.

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8

Xiang, Changyuan, Yongxin Lan, Qinghua Yan, and Changqing Xu. "The Outer-Planar Anti-Ramsey Number of Matchings." Symmetry 14, no. 6 (2022): 1252. http://dx.doi.org/10.3390/sym14061252.

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A subgraph H of an edge-colored graph G is called rainbow if all of its edges have different colors. Let ar(G,H) denote the maximum positive integer t, such that there is a t-edge-colored graph G without any rainbow subgraph H. We denote by kK2 a matching of size k and On the class of all maximal outer-planar graphs on n vertices, respectively. The outer-planar anti-Ramsey number of graph H, denoted by ar(On,H), is defined as max{ar(On,H)|On∈On}. It seems nontrivial to determine the exact values for ar(On,H) because most maximal outer-planar graphs are asymmetry. In this paper, we obtain that

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9

Jin, Zemin, Rui Yu, and Yuefang Sun. "Anti-Ramsey number of matchings in outerplanar graphs." Discrete Applied Mathematics 345 (March 2024): 125–35. http://dx.doi.org/10.1016/j.dam.2023.11.049.

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10

Jin, Zemin, Oothan Nweit, Kaijun Wang, and Yuling Wang. "Anti-Ramsey numbers for matchings in regular bipartite graphs." Discrete Mathematics, Algorithms and Applications 09, no. 02 (2017): 1750019. http://dx.doi.org/10.1142/s1793830917500197.

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Let [Formula: see text] be a family of graphs. The anti-Ramsey number [Formula: see text] for [Formula: see text] in the graph [Formula: see text] is the maximum number of colors in an edge coloring of [Formula: see text] that does not have any rainbow copy of any graph in [Formula: see text]. In this paper, we consider the anti-Ramsey number for matchings in regular bipartite graphs and determine its value under several conditions.

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11

Ding, Jili, Hong Bian, and Haizheng Yu. "Anti-Ramsey Numbers in Complete k-Partite Graphs." Mathematical Problems in Engineering 2020 (September 7, 2020): 1–5. http://dx.doi.org/10.1155/2020/5136104.

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The anti-Ramsey number ARG,H is the maximum number of colors in an edge-coloring of G such that G contains no rainbow subgraphs isomorphic to H. In this paper, we discuss the anti-Ramsey numbers ARKp1,p2,…,pk,Tn, ARKp1,p2,…,pk,ℳ, and ARKp1,p2,…,pk,C of Kp1,p2,…,pk, where Tn,ℳ, and C denote the family of all spanning trees, the family of all perfect matchings, and the family of all Hamilton cycles in Kp1,p2,…,pk, respectively.

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12

Gorgol, Izolda. "Avoiding rainbow 2-connected subgraphs." Open Mathematics 15, no. 1 (2017): 393–97. http://dx.doi.org/10.1515/math-2017-0035.

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Abstract While defining the anti-Ramsey number Erdős, Simonovits and Sós mentioned that the extremal colorings may not be unique. In the paper we discuss the uniqueness of the colorings, generalize the idea of their construction and show how to use it to construct the colorings of the edges of complete split graphs avoiding rainbow 2-connected subgraphs. These colorings give the lower bounds for adequate anti-Ramsey numbers.

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13

Jin, Zemin, Kangyun Zhong, and Yuefang Sun. "Anti-Ramsey Number of Triangles in Complete Multipartite Graphs." Graphs and Combinatorics 37, no. 3 (2021): 1025–44. http://dx.doi.org/10.1007/s00373-021-02302-z.

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14

Lu, Linyuan, and Zhiyu Wang. "Anti-Ramsey Number of Edge-Disjoint Rainbow Spanning Trees." SIAM Journal on Discrete Mathematics 34, no. 4 (2020): 2346–62. http://dx.doi.org/10.1137/19m1299876.

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15

Guo, Mingyang, Hongliang Lu, and Xing Peng. "Anti-Ramsey Number of Matchings in 3-Uniform Hypergraphs." SIAM Journal on Discrete Mathematics 37, no. 3 (2023): 1970–87. http://dx.doi.org/10.1137/22m1503178.

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16

Yousifi, Noorya. "A short proof of anti-Ramsey number for cycles." International Journal of Multidisciplinary Research and Growth Evaluation 2, no. 3 (2021): 108–9. http://dx.doi.org/10.54660/.ijmrge.2021.2.3.108-109.

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Ramsey's theorem states that there exists a least positive integer R(r, s) for which every blue-red edge colouring of the complete graph on R(r, s) vertices contains a blue clique on r vertices or a red clique on s vertices. This work contains a simplified proof of Anti-Ramsey theorem for cycles. If there is an edge e between H and H0, incident to, say, some v ∈ H of color from NEWc(v), then we can make H and H0 connected by adding the edge e and deleting some edge incident to v of the same color as e in H, so the resulting graph G˜ has a connected component of order ≥ 2( k+1/2 ), which contra

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17

罗, 冬连. "The Anti-Ramsey Number of Unconnected Graphs in Plane Triangulation Graphs." Advances in Applied Mathematics 12, no. 06 (2023): 3030–38. http://dx.doi.org/10.12677/aam.2023.126304.

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18

Tang, Yucong, Tong Li, and Guiying Yan. "Anti-Ramsey number of disjoint union of star-like hypergraphs." Discrete Mathematics 347, no. 4 (2024): 113748. http://dx.doi.org/10.1016/j.disc.2023.113748.

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19

Xue, Yisai, Erfang Shan, and Liying Kang. "Anti-Ramsey number of matchings in r-partite r-uniform hypergraphs." Discrete Mathematics 345, no. 4 (2022): 112782. http://dx.doi.org/10.1016/j.disc.2021.112782.

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20

Jin, Zemin, Yite Wang, Huawei Ma, and Huaping Wang. "Computing the anti-Ramsey number for trees in complete tripartite graph." Applied Mathematics and Computation 456 (November 2023): 128151. http://dx.doi.org/10.1016/j.amc.2023.128151.

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21

Jin, Zemin, Weijia Zhou, Ting Yu, and Yuefang Sun. "Anti-Ramsey number for perfect matchings in 3-regular bipartite graphs." Discrete Mathematics 347, no. 7 (2024): 114011. http://dx.doi.org/10.1016/j.disc.2024.114011.

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22

Lu, Linyuan, Andrew Meier, and Zhiyu Wang. "Anti-Ramsey Number of Edge-Disjoint Rainbow Spanning Trees in All Graphs." SIAM Journal on Discrete Mathematics 37, no. 2 (2023): 1162–72. http://dx.doi.org/10.1137/21m1428121.

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23

Jiang, T., and D. West. "On the Erdős–Simonovits–Sós Conjecture about the Anti-Ramsey Number of a Cycle." Combinatorics, Probability and Computing 12, no. 5-6 (2003): 585–98. http://dx.doi.org/10.1017/s096354830300590x.

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Given a positive integer n and a family of graphs, let denote the maximum number of colours in an edge-colouring of such that no subgraph of belonging to has distinct colours on its edges. Erdös, Simonovits and Sós [6] conjectured for fixed k with that . This has been proved for . For general k, in this paper we improve the previous bound of to . For even k, we further improve it to . We also prove that , which is sharp.

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24

Budden, Mark, and William Stiles. "Anti-Ramsey Hypergraph Numbers." Electronic Journal of Graph Theory and Applications 9, no. 2 (2021): 397. http://dx.doi.org/10.5614/ejgta.2021.9.2.12.

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25

Gilboa, Shoni, and Dan Hefetz. "On degree anti-Ramsey numbers." European Journal of Combinatorics 60 (February 2017): 31–41. http://dx.doi.org/10.1016/j.ejc.2016.09.002.

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26

Alon, Noga. "Size and Degree Anti-Ramsey Numbers." Graphs and Combinatorics 31, no. 6 (2015): 1833–39. http://dx.doi.org/10.1007/s00373-015-1583-9.

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27

Chen, Gang, Yongxin Lan, and Zi-Xia Song. "Planar anti-Ramsey numbers of matchings." Discrete Mathematics 342, no. 7 (2019): 2106–11. http://dx.doi.org/10.1016/j.disc.2019.04.005.

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28

Axenovich, Maria, Kolja Knauer, Judith Stumpp, and Torsten Ueckerdt. "Online and size anti-Ramsey numbers." Journal of Combinatorics 5, no. 1 (2014): 87–114. http://dx.doi.org/10.4310/joc.2014.v5.n1.a4.

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29

Jiang, Tao. "Anti-Ramsey Numbers of Subdivided Graphs." Journal of Combinatorial Theory, Series B 85, no. 2 (2002): 361–66. http://dx.doi.org/10.1006/jctb.2001.2105.

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30

Axenovich, Maria, Tao Jiang, and André Kündgen. "Bipartite anti-Ramsey numbers of cycles." Journal of Graph Theory 47, no. 1 (2004): 9–28. http://dx.doi.org/10.1002/jgt.20012.

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31

Wu, Fangfang, Shenggui Zhang, Binlong Li, and Jimeng Xiao. "Anti-Ramsey numbers for vertex-disjoint triangles." Discrete Mathematics 346, no. 1 (2023): 113123. http://dx.doi.org/10.1016/j.disc.2022.113123.

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32

Gorgol, Izolda. "Anti-Ramsey numbers in complete split graphs." Discrete Mathematics 339, no. 7 (2016): 1944–49. http://dx.doi.org/10.1016/j.disc.2015.10.038.

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33

Li, Yibo, Huiqing Liu, and Xiaolan Hu. "Anti-Ramsey numbers for cycles in n-prisms." Discrete Applied Mathematics 322 (December 2022): 1–8. http://dx.doi.org/10.1016/j.dam.2022.07.029.

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34

Xie, Tian-Ying, and Long-Tu Yuan. "On the anti-Ramsey numbers of linear forests." Discrete Mathematics 343, no. 12 (2020): 112130. http://dx.doi.org/10.1016/j.disc.2020.112130.

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35

Lan, Yongxin, Yongtang Shi, and Zi-Xia Song. "Planar anti-Ramsey numbers of paths and cycles." Discrete Mathematics 342, no. 11 (2019): 3216–24. http://dx.doi.org/10.1016/j.disc.2019.06.034.

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36

Gorgol, Izolda, and Agnieszka Görlich. "Anti-Ramsey numbers for disjoint copies of graphs." Opuscula Mathematica 37, no. 4 (2017): 567. http://dx.doi.org/10.7494/opmath.2017.37.4.567.

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37

Jiang, Tao, and Oleg Pikhurko. "Anti-Ramsey numbers of doubly edge-critical graphs." Journal of Graph Theory 61, no. 3 (2009): 210–18. http://dx.doi.org/10.1002/jgt.20380.

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38

Gilboa, Shoni, and Yehuda Roditty. "Anti-Ramsey Numbers of Graphs with Small Connected Components." Graphs and Combinatorics 32, no. 2 (2015): 649–62. http://dx.doi.org/10.1007/s00373-015-1581-y.

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39

Gu, Ran, Jiaao Li, and Yongtang Shi. "Anti-Ramsey Numbers of Paths and Cycles in Hypergraphs." SIAM Journal on Discrete Mathematics 34, no. 1 (2020): 271–307. http://dx.doi.org/10.1137/19m1244950.

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40

Ryder, Alex B., Jeanne E. Hendrickson, and Christopher A. Tormey. "Chronic Inflammatory Autoimmune Disorders Are a Risk Factor for Blood Group Alloimmunization in Transfused Patients." Blood 124, no. 21 (2014): 4294. http://dx.doi.org/10.1182/blood.v124.21.4294.4294.

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Abstract Background: Alloimmunization to red blood cell (RBC) antigens is a clinically-significant problem, but the mechanisms underlying antibody induction remain poorly understood. Data from murine models has suggested that inflammation can promote blood group alloimmunization. To our knowledge, only one group (Ramsey & Smietana, Transfusion 1995;35:582) has examined the influence of inflammation on RBC alloimmunization; however, study subjects were predominantly female, making it difficult to determine the contribution of inflammation towards transfusion-related alloimmunization. Thus,

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41

Zhang, Meiqiao, and Fengming Dong. "Anti-Ramsey numbers for trees in complete multi-partite graphs." Discrete Mathematics 345, no. 12 (2022): 113100. http://dx.doi.org/10.1016/j.disc.2022.113100.

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42

Liu, Huiqing, Mei Lu, and Shunzhe Zhang. "Anti-Ramsey numbers for cycles in the generalized Petersen graphs." Applied Mathematics and Computation 430 (October 2022): 127277. http://dx.doi.org/10.1016/j.amc.2022.127277.

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43

Jin, Zemin. "Anti-Ramsey numbers for matchings in 3-regular bipartite graphs." Applied Mathematics and Computation 292 (January 2017): 114–19. http://dx.doi.org/10.1016/j.amc.2016.07.037.

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44

Jungic, V., J. Licht, M. Mahdian, J. Nesetril, and R. Radoicic. "Rainbow Arithmetic Progressions and Anti-Ramsey Results." Combinatorics, Probability and Computing 12, no. 5-6 (2003): 599–620. http://dx.doi.org/10.1017/s096354830300587x.

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The van der Waerden theorem in Ramsey theory states that, for every k and t and sufficiently large N, every k-colouring of [N] contains a monochromatic arithmetic progression of length t. Motivated by this result, Radoičić conjectured that every equinumerous 3-colouring of [3n] contains a 3-term rainbow arithmetic progression, i.e., an arithmetic progression whose terms are coloured with distinct colours. In this paper, we prove that every 3-colouring of the set of natural numbers for which each colour class has density more than 1/6, contains a 3-term rainbow arithmetic progression. We also p

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45

Pei, Yifan, Yongxin Lan, and Hua He. "Improved bounds for anti-Ramsey numbers of matchings in outer-planar graphs." Applied Mathematics and Computation 418 (April 2022): 126843. http://dx.doi.org/10.1016/j.amc.2021.126843.

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46

Fang, Chunqiu, Ervin Győri, Binlong Li, and Jimeng Xiao. "The anti-Ramsey numbers of C3 and C4 in complete r-partite graphs." Discrete Mathematics 344, no. 11 (2021): 112540. http://dx.doi.org/10.1016/j.disc.2021.112540.

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47

Chandran, L. Sunil, Talha Hashim, Dalu Jacob, Rogers Mathew, Deepak Rajendraprasad, and Nitin Singh. "New bounds on the anti-Ramsey numbers of star graphs via maximum edge q-coloring." Discrete Mathematics 347, no. 4 (2024): 113894. http://dx.doi.org/10.1016/j.disc.2024.113894.

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48

Fischer, Melissa A., Maria Arrate, Merrida A. Childress, et al. "Variable Response to BCL2 Inhibition in MDS Is Enhanced across MDS Subtypes with Synergistic Combination of BCL2+MCL1 Inhibition." Blood 134, Supplement_1 (2019): 2982. http://dx.doi.org/10.1182/blood-2019-126578.

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Myelodysplastic syndromes (MDS) are heterogeneous bone marrow failure neoplasms marked by cytopenias, reduced quality of life and predilection to transform into AML. While several treatments for AML have recently been approved, the available treatments for MDS are lacking, and adaptation of AML therapy to MDS is complicated. This is due, in part, to the heterogeneity of MDS. Despite this heterogeneity, most clonal cells in MDS have an imbalance of mitochondrial-controlled BCL2 family proteins resulting in dysregulated apoptosis. These anti- (or pro-) apoptotic proteins compete for ligand to bl

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49

Saud Sunny, S., N. Islam, and A. T. M. Asaduzzaman. "AB0546 DETERMINANTS OF VASCULITIS IN SYSTEMIC LUPUS ERYTHEMATOSUS PATIENTS." Annals of the Rheumatic Diseases 81, Suppl 1 (2022): 1400.2–1400. http://dx.doi.org/10.1136/annrheumdis-2022-eular.4274.

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BackgroundAmong the manifestations of SLE, vasculitic presentation is common. This study was aimed to identify the predictors of vasculitis in SLE patients.ObjectivesTo identify the determinants of vasculitis in SLE patients.MethodsThe study was conducted in the Department of Rheumatology, BSMMU, Dhaka from December 2019 to January 2021. A total 168 consecutive confirmed cases of SLE patients were enrolled. The patients were evaluated for the features of vasculitic rashes, digital gangrene, mesenteric vasculitis, mononeuritis multiplex. The cutaneous vasculitis was confirmed by a dermatologist

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50

Cook, Katherine L., Ramsey Jenshcke, Karen Corleto, et al. "Abstract PS07-08: Bazedoxifene plus conjugated estrogen reduces mammary proliferation markers and improves adipocyte size, gut microbiome, and metabolic health: Findings from a preclinical model of obesity and breast cancer risk." Cancer Research 84, no. 9_Supplement (2024): PS07–08—PS07–08. http://dx.doi.org/10.1158/1538-7445.sabcs23-ps07-08.

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Abstract Background: Many women at high risk for breast cancer will not take tamoxifen or aromatase inhibitors for cancer prevention due to concern of side effects including hot flashes. Further, tamoxifen has detrimental metabolic effects in some overweight/obese women. Duavee®, a tissue-selective complex of bazedoxifene + conjugated estrogen, is FDA-approved for relief of hot-flashes and prevention of osteoporosis. Preclinical studies suggest favorable metabolic effects and potential for breast cancer risk reduction. In a single arm clinical trial, BZA+CE reduced Ki-67 and mammographic densi

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