Game chromatic number of strong product graphs

Hikoe Enomoto, Jun Fujisawa, Naoki Matsumoto

Research output: Contribution to journalArticlepeer-review

Abstract

The graph coloring game is a two-player game in which the two players properly color an uncolored vertex of G alternately. The first player wins the game if all vertices of G are colored, and the second wins otherwise. The game chromatic number of a graph G is the minimum integer k such that the first player has a winning strategy for the graph coloring game on G with k colors. There is a lot of literature on the game chromatic number of graph products, e.g., the Cartesian product and the lexicographic product. In this paper, we investigate the game chromatic number of the strong product of graphs, which is one of major graph products. In particular, we completely determine the game chromatic number of the strong product of a double star and a complete graph. Moreover, we estimate the game chromatic number of some King's graphs, which are the strong products of two paths.

Original languageEnglish
Article number113162
JournalDiscrete Mathematics
Volume346
Issue number1
DOIs
Publication statusPublished - 2023 Jan

Keywords

  • Game chromatic number
  • King's graph
  • Strong product

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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