Game coloring the Cartesian product of graphs

  • Authors:

  • Xuding Zhu

  • Affiliations:

  • Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan and National Center for Theoretical Sciences, Taiwan

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2008

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Abstract

This article proves the following result: Let G and G′ be graphs of orders n and n′, respectively. Let G* be obtained from G by adding to each vertex a set of n′ degree 1 neighbors. If G* has game coloring number m and G′ has acyclic chromatic number k, then the Cartesian product G□G′ has game chromatic number at most k(k + m - 1). As a consequence, the Cartesian product of two forests has game chromatic number at most 10, and the Cartesian product of two planar graphs has game chromatic number at most 105. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 261–278, 2008