ACYCLIC EDGE-COLORING OF PLANAR GRAPHS

被引：34

作者：

Basavaraju, Manu ^{[1
]}

Chandran, L. Sunil ^{[1
]}

Cohen, Nathann ^{[2
,3
]}

Havet, Frederic ^{[2
,3
]}

Mueller, Tobias ^{[4
]}

机构：

[1] Indian Inst Sci, Comp Sci & Automat Dept, Bangalore 560012, Karnataka, India

[2] UNSA, CNRS, I3S, Projet Mascotte, F-06902 Sophia Antipolis, France

[3] INRIA, F-06902 Sophia Antipolis, France

[4] Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math, IL-69978 Tel Aviv, Israel

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2011年 / 25卷 / 02期

关键词：

edge-coloring; planar graphs; bounded density graphs; CHROMATIC NUMBER;

D O I：

10.1137/090776676

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A proper edge-coloring with the property that every cycle contains edges of at least three distinct colors is called an acyclic edge-coloring. The acyclic chromatic index of a graph G, denoted. chi'(alpha)(G), is the minimum k such that G admits an acyclic edge-coloring with k colors. We conjecture that if G is planar and Delta(G) is large enough, then chi'(alpha) (G) = Delta (G). We settle this conjecture for planar graphs with girth at least 5. We also show that chi'(alpha) (G) <= Delta (G) + 12 for all planar G, which improves a previous result by Fiedorowicz, Haluszczak, and Narayan [Inform. Process. Lett., 108 (2008), pp. 412-417].

引用

页码：463 / 478

页数：16

共 50 条

[21] Local conditions for planar graphs of acyclic edge coloring
Zhang, Wenwen
[J]. JOURNAL OF APPLIED MATHEMATICS AND COMPUTING, 2022, 68 (02) : 721 - 738
[22] Strong edge-coloring of planar graphs with girth at least seven
Yuan, Jiaxin
Huang, Mingfang
[J]. ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2024, (51): : 295 - 304
[23] Acyclic Edge Coloring of IC-planar Graphs
Song, Wen-yao
Duan, Yuan-yuan
Wang, Juan
Miao, Lian-ying
[J]. ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2020, 36 (03): : 581 - 589
[24] A GENERALIZATION OF EDGE-COLORING IN GRAPHS
HAKIMI, SL
KARIV, O
[J]. JOURNAL OF GRAPH THEORY, 1986, 10 (02) : 139 - 154
[25] Edge-Coloring of Split Graphs
de Almeida, Sheila Morais
de Mello, Celia Picinin
Morgana, Aurora
[J]. ARS COMBINATORIA, 2015, 119 : 363 - 375
[26] New linear-time algorithms for edge-coloring planar graphs
Cole, Richard
Kowalik, Lukasz
[J]. ALGORITHMICA, 2008, 50 (03) : 351 - 368
[27] New Linear-Time Algorithms for Edge-Coloring Planar Graphs
Richard Cole
Łukasz Kowalik
[J]. Algorithmica, 2008, 50 : 351 - 368
[28] Acyclic edge-coloring using entropy compression
Esperet, Louis
Parreau, Aline
[J]. EUROPEAN JOURNAL OF COMBINATORICS, 2013, 34 (06) : 1019 - 1027
[29] Acyclic Edge Coloring of Triangle-Free Planar Graphs
Basavaraju, Manu
Chandran, L. Sunil
[J]. JOURNAL OF GRAPH THEORY, 2012, 71 (04) : 365 - 385
[30] Acyclic Edge Coloring of Planar Graphs without Adjacent Triangles
Dezheng XIE 1
2.School of Mathematics and Computer Science
[J]. Journal of Mathematical Research with Applications, 2012, (04) : 407 - 414

← 1 2 3 4 5 →