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author:

Hou, Jianfeng (Hou, Jianfeng.) [1] (Scholars:侯建锋) | Wu, Shufei (Wu, Shufei.) [2]

Indexed by:

Scopus SCIE CSCD

Abstract:

Let G be a graph of maximum degree Delta. A proper vertex coloring of G is acyclic if there is no bichromatic cycle. It was proved by Alon et al. [Acyclic coloring of graphs. Random Structures Algorithms, 1991, 2(3): 277-288] that G admits an acyclic coloring with O(Delta(4/3)) colors and a proper coloring with O(Delta((k-1)/(k-2))) colors such that no path with k vertices is bichromatic for a fixed integer k a parts per thousand yen 5. In this paper, we combine above two colorings and show that if k a parts per thousand yen 5 and G does not contain cycles of length 4, then G admits an acyclic coloring with O(Delta((k-1)/(k-2))) colors such that no path with k vertices is bichromatic.

Keyword:

acyclic Coloring entropy compression path

Community:

  • [ 1 ] [Hou, Jianfeng]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350003, Peoples R China
  • [ 2 ] [Wu, Shufei]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350003, Peoples R China

Reprint 's Address:

  • 毋述斐

    [Wu, Shufei]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350003, Peoples R China

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Source :

FRONTIERS OF MATHEMATICS IN CHINA

ISSN: 1673-3452

Year: 2015

Issue: 6

Volume: 10

Page: 1343-1354

0 . 4 4 4

JCR@2015

0 . 8 0 0

JCR@2023

JCR Journal Grade:4

CAS Journal Grade:4

Cited Count:

WoS CC Cited Count: 5

SCOPUS Cited Count: 5

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 6

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