A note on acyclic vertex-colorings

被引：7

作者：

Sereni, Jean-Sebastien ^{[1
]}

Volec, Jan ^{[2
,3
,4
]}

机构：

[1] CNRS, LORIA, Vandoeuvre Les Nancy, France

[2] ETH, Dept Math, CH-8092 Zurich, Switzerland

[3] Univ Warwick, Inst Math, Coventry CV4 7AL, W Midlands, England

[4] Univ Warwick, DIMAP, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF COMBINATORICS | 2016年 / 7卷 / 04期

关键词：

Acyclic coloring; entropy compression; local lemma;

D O I：

10.4310/JOC.2016.v7.n4.a8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that the acyclic chromatic number of a graph with maximum degree Delta is less than 2.835 Delta(4/3) + Delta. This improves the previous upper bound, which was 50 Delta(4/3). To do so, we draw inspiration from works by Alon, McDiarmid & Reed and by Esperet & Parreau.

引用

页码：725 / 737

页数：13

共 50 条

[21] ACYCLIC COLORINGS OF PLANAR GRAPHS
GRUNBAUM, B
ISRAEL JOURNAL OF MATHEMATICS, 1973, 14 (04) : 390 - 408
[22] On acyclic colorings of graphs on surfaces
Alon, N
Mohar, B
Sanders, DP
ISRAEL JOURNAL OF MATHEMATICS, 1996, 94 : 273 - 283
[23] ACYCLIC COLORINGS OF PLANAR GRAPHS
GRUNBAUM, B
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 19 (07): : A816 - A816
[24] PAPER OF GRUNBAUM ON ACYCLIC COLORINGS
KOSTOCHKA, AV
MELNIKOV, LS
DISCRETE MATHEMATICS, 1976, 14 (04) : 403 - 406
[25] ACYCLIC COLORINGS OF PLANAR GRAPHS
BORODIN, OV
DISCRETE MATHEMATICS, 1979, 25 (03) : 211 - 236
[26] Acyclic and star colorings of cographs
Lyons, Andrew
DISCRETE APPLIED MATHEMATICS, 2011, 159 (16) : 1842 - 1850
[27] VERTEX RAINBOW COLORINGS OF GRAPHS
Fujie-Okamoto, Futaba
Kolasinski, Kyle
Lin, Jianwei
Zhang, Ping
DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2012, 32 (01) : 63 - 80
[28] VERTEX COLORINGS WITHOUT ISOLATES
MAURER, SB
JOURNAL OF COMBINATORIAL THEORY SERIES B, 1979, 27 (03) : 294 - 319
[29] BOUNDED VERTEX COLORINGS OF GRAPHS
HANSEN, P
HERTZ, A
KUPLINSKY, J
DISCRETE MATHEMATICS, 1993, 111 (1-3) : 305 - 312
[30] Vertex colorings with a distance restriction
Chen, GT
Gyarfas, A
Schelp, RH
DISCRETE MATHEMATICS, 1998, 191 (1-3) : 65 - 82

← 1 2 3 4 5 →