Game Chromatic Number of Some Regular Graphs

• 作者: Khaled Alshehada Ramy Shaheen Ziad Kanaya
• 来源期刊: 离散数学期刊(英文)
• 学科: 数学
• 关键词: GAME CHROMATIC Number CIRCULANT GRAPH GENERALIZED Petersen GRAPHS
• 年，卷（期）: lssxqkyw_2019,（4）
• 页码范围: 159-164
• 页数: 6页
• 分类号: O15

摘要

Let G be a graph and k be a positive integer. We consider a game with two players Alice and Bob who alternate in coloring the vertices of G with a set of k colors. In every turn, one vertex will be chosen by one player. Alice’s goal is to color all vertices with the k colors, while Bob’s goal is to prevent her. The game chromatic number denoted by?χg(G), is the smallest k such that Alice has a winning strategy with k colors. In this paper, we determine the game chromatic number?χg of circulant graphs?Cn(1,2), , and generalized Petersen graphs GP(n,2), GP(n,3).