The graph distance game and some graph operations

Abstract In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exact results for special graphs.

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

[2]  Xuding Zhu,et al.  Game chromatic number of outerplanar graphs , 1999, J. Graph Theory.

[3]  John Y. Kim.  The incidence game chromatic number of paths and subgraphs of wheels , 2011, Discret. Appl. Math..

[4]  Paul Dorbec,et al.  The domination game played on unions of graphs , 2015, Discret. Math..

[5]  Iztok Peterin,et al.  Game chromatic number of Cartesian product graphs , 2007, Electron. Notes Discret. Math..

[6]  Elzbieta Sidorowicz.  The game chromatic number and the game colouring number of cactuses , 2007, Inf. Process. Lett..

[7]  E. Berlekamp,et al.  Winning Ways for Your Mathematical Plays , 1983 .

[8]  Xuding Zhu,et al.  Game coloring the Cartesian product of graphs , 2008, J. Graph Theory.

[9]  Csilla Bujtás.  Domination game on forests , 2015, Discret. Math..

[10]  Peter J. Slater,et al.  Competition Parameters of a Graph , 2007 .

[11]  Jorge Nuno Silva,et al.  Mathematical Games , 1959, Nature.

[12]  Matthew Walsh.  The Competition Chromatic Numbers of a Graph , 2003 .

[13]  Xuding Zhu,et al.  Game colouring of the square of graphs , 2009, Discret. Math..

[14]  Sandi Klavzar,et al.  Domination Game and an Imagination Strategy , 2010, SIAM J. Discret. Math..

[15]  Honghai Xu,et al.  The graph distance game , 2011 .

[16]  Sandi Klavzar,et al.  Domination game played on trees and spanning subgraphs , 2013, Discret. Math..

[17]  Aviezri S. Fraenkel,et al.  Combinatorial Games: selected Bibliography with a Succinct Gourmet Introduction , 2012 .

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

[19]  J. Beck.  Combinatorial Games: Tic-Tac-Toe Theory , 2008 .

[20]  Saumyendra Sengupta,et al.  Graphs and Digraphs , 1994 .

[21]  deXuding Zhu.  Game Chromatic Number of Graphs , 1998 .

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

[23]  Mehdi Behzad,et al.  Graphs and Digraphs , 1981, The Mathematical Gazette.