Equitable colorings of K4-minor-free graphs

被引：0

作者：

de Joannis de Verclos R. ^{[1
]}

Sereni J.-S. ^{[2
]}

机构：

[1] Laboratoire G-SCOP, C.N.R.S. et Univ. Grenoble Alpes, Grenoble

[2] Centre National de la Recherche Scientifique, CSTB (ICube), Strasbourg

来源：

| 2017年 / Brown University卷 / 21期

关键词：

D O I：

10.7155/jgaa.00451

中图分类号：

O144 [集合论]; O157 [组合数学（组合学）];

学科分类号：

070104 ;

摘要：

We demonstrate that for every positive integer ∆, every K4-minor-free graph with maximum degree ∆ admits an equitable coloring with k colors where k ≥∆+3/2. This bound is tight and confirms a conjecture by Zhang and Wu. We do not use the discharging method but rather exploit decomposition trees of K4-minor-free graphs. © 2017, Brown University. All rights reserved.

引用

页码：1091 / 1105

页数：14

共 50 条

[1] Homomorphism bounds of signed bipartite K4-minor-free graphs and edge-colorings of 2k-regular K4-minor-free multigraphs
Beaudou, Laurent
Foucaud, Florent
Naserasr, Reza
DISCRETE APPLIED MATHEMATICS, 2019, 261 : 40 - 51
[2] Precoloring Extension for K4-Minor-Free Graphs
Pruchnewski, Ania
Voigt, Margit
JOURNAL OF GRAPH THEORY, 2009, 60 (04) : 284 - 294
[3] Toughness and spanning trees in K4-minor-free graphs
Ellingham, M. N.
Shan, Songling
Ye, Dong
Zha, Xiaoya
JOURNAL OF GRAPH THEORY, 2021, 96 (03) : 379 - 402
[4] K4-MINOR-FREE INDUCED SUBGRAPHS OF SPARSE CONNECTED GRAPHS
Joret, Gwenael
Wood, David R.
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2018, 32 (01) : 123 - 147
[5] Bounding the chromatic number of squares of K4-minor-free graphs
Civan, Yusuf
Deniz, Zakir
Yetim, Mehmet Akif
DISCRETE MATHEMATICS, 2019, 342 (07) : 1894 - 1903
[6] Extremal K4-minor-free graphs without short cycles
Barat, Janos
PERIODICA MATHEMATICA HUNGARICA, 2023, 86 (01) : 108 - 114
[7] COUNTING HOMOMORPHISMS TO K4-MINOR-FREE GRAPHS, MODULO 2
Focke, Jacob
Goldberg, Leslie Ann
Roth, Marc
Zivny, Stanislav
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2021, 35 (04) : 2749 - 2814
[8] Strict neighbor-distinguishing index of K4-minor-free graphs
Gu, Jing
Wang, Yiqiao
Wang, Weifan
Zheng, Lina
DISCRETE APPLIED MATHEMATICS, 2023, 329 : 87 - 95
[9] A Brooks-type bound for squares of K4-minor-free graphs
Kostochka, Alexandr V.
Ozkahya, Lale
Woodall, Douglas R.
DISCRETE MATHEMATICS, 2009, 309 (23-24) : 6572 - 6584
[10] Homomorphism bounds and edge-colourings of K4-minor-free graphs
Beaudou, Laurent
Foucaud, Florent
Naserasr, Reza
JOURNAL OF COMBINATORIAL THEORY SERIES B, 2017, 124 : 128 - 164

← 1 2 3 4 5 →