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author:

Kierstead, H. A. (Kierstead, H. A..) [1] | Yang, Chung-Ying (Yang, Chung-Ying.) [2] | Yang, Daqing (Yang, Daqing.) [3] | Zhu, Xuding (Zhu, Xuding.) [4]

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Abstract:

Suppose G = (V, E) is a graph and F is a colouring of its edges (not necessarily proper) that uses the colour set X. In an adapted colouring game, Alice and Bob alternately colour uncoloured vertices of G with colours from X. A partial colouring c of the vertices of G is legal if there is no edge e = xy such that c(x) = c(y) = F(e). In the process of the game, each partial colouring must be legal. If eventually all the vertices of Care coloured, then Alice wins the game. Otherwise, Bob wins the game. The adapted game chromatic number of a graph G, denoted by chi(adg)(G), is the minimum number of colours needed to ensure that for any edge colouring F of G, Alice has a winning strategy for the game. This paper studies the adapted game chromatic number of various classes of graphs. We prove that the maximum adapted game chromatic number of trees is 3, the maximum adapted game chromatic number of outerplanar graphs is 5, the adapted game chromatic number of partial k-trees is at most 2k+1, and the adapted game chromatic number of planar graphs is at most 11. (C) 2011 Elsevier Ltd. All rights reserved.

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  • [ 1 ] [Kierstead, H. A.]Arizona State Univ, Dept Math & Stat, Tempe, AZ 85287 USA
  • [ 2 ] [Yang, Chung-Ying]Natl Sun Yat Sen Univ, Dept Appl Math, Kaohsiung, Taiwan
  • [ 3 ] [Yang, Daqing]Fuzhou Univ, Ctr Discrete Math, Fuzhou 350002, Fujian, Peoples R China
  • [ 4 ] [Zhu, Xuding]Zhejiang Normal Univ, Dept Math, Jinhua, Peoples R China

Reprint 's Address:

  • [Kierstead, H. A.]Arizona State Univ, Dept Math & Stat, Tempe, AZ 85287 USA

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Source :

EUROPEAN JOURNAL OF COMBINATORICS

ISSN: 0195-6698

Year: 2012

Issue: 4

Volume: 33

Page: 435-445

0 . 6 5 8

JCR@2012

1 . 0 0 0

JCR@2023

ESI Discipline: MATHEMATICS;

JCR Journal Grade:2

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count: 6

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 0

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