论文信息 - On the game chromatic number of splitting graphs of path and cycle

On the game chromatic number of splitting graphs of path and cycle

Abstract Given a graph G and an integer k , two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins if at the end of the game all the vertices of G are colored. The game chromatic number χ g ( G ) is the minimum k for which the first player has a winning strategy. In this study, we prove that the game chromatic number of the splitting graphs of the path P n and cycle C n for n ≥ 5 is 4. We also answer a question posed by Xuding Zhu in [12] for the splitting graphs of path P n and n -cycle for all n ≥ 3

Usman Ali | Ghulam Abbas | Muhammad Saleem Akhtar | Mutahira Batool

[1] Jaroslav Nesetril,et al. On the Oriented Game Chromatic Number , 2001, Electron. J. Comb..

[2] Xuding Zhu,et al. The Map-Coloring Game , 2007, Am. Math. Mon..

[3] Xuding Zhu. The Game Coloring Number of Planar Graphs , 1999, J. Comb. Theory, Ser. B.

[4] Xuding Zhu,et al. A bound for the game chromatic number of graphs , 1999, Discret. Math..

[5] Xuding Zhu,et al. Refined activation strategy for the marking game , 2008, J. Comb. Theory B.

[6] Stephan Dominique Andres. The game chromatic index of forests of maximum degree Delta>=5 , 2006, Discret. Appl. Math..

[7] Charmaine Sia,et al. The Game Chromatic Number of Some Families of Cartesian Product Graphs , 2009 .

[8] Xuding Zhu,et al. Game chromatic number of outerplanar graphs , 1999 .

[9] Hal A. Kierstead,et al. A simple competitive graph coloring algorithm III , 2004, J. Comb. Theory B.

[10] Xuding Zhu,et al. Game chromatic index of k-degenerate graphs , 2001 .

[11] U. Faigle,et al. On the game chromatic number of some classes of graphs , 1991 .