Acyclic colourings of planar graphs with large girth

被引：54
|
作者：
Borodin, OV [1 ]
Kostochka, AV
Woodall, DR
机构：
[1] Russian Acad Sci, Inst Math, Novosibirsk 630090, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
[3] Univ Nottingham, Dept Math, Nottingham NG7 2RD, England
来源：
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 1999年 / 60卷
基金：
英国工程与自然科学研究理事会;
关键词：
D O I：
10.1112/S0024610799007942
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A proper vertex-colouring of a graph is acidic if there are no 2-coloured cycles. It is known that every planar graph is acyclically 5-colourable. and that there are planar graphs with acyclic chromatic number chi (a) = 5 and girth g = 4. It is proved here that a planar graph satisfies chi (a) less than or equal to 4 if g greater than or equal to 5 and chi less than or equal to 3 if g greater than or equal to 7.
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页码：344 / 352
页数：9
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