An upper bound on the extremal version of Hajnal's triangle-free game

A game starts with the empty graph on n vertices, and two players alternate adding edges to the graph. Only moves which do not create a triangle are valid. The game ends when a maximal triangle-free graph is reached. The goal of one player is to end the game as soon as possible, while the other player is trying to prolong the game. With optimal play, the length of the game (number of edges played) is called the K 3 game saturation number.In this paper we prove an upper bound for this number.

[1]  James M. Carraher,et al.  The Game Saturation Number of a Graph , 2017, J. Graph Theory.

[2]  Ago-Erik Riet,et al.  F-saturation games , 2014, Discret. Math..

[3]  Pawel Pralat,et al.  Game brush number , 2014, Discret. Appl. Math..

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

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

[6]  Daniel W. Cranston,et al.  Game matching number of graphs , 2013, Discret. Appl. Math..

[7]  Pawel Pralat,et al.  The first player wins the one-colour triangle avoidance game on 16 vertices , 2012, Discuss. Math. Graph Theory.

[8]  Ákos Seress,et al.  On Hajnal's triangle-free game , 1992, Graphs Comb..

[9]  T. Bohman.  The triangle-free process , 2008, 0806.4375.

[10]  Anthony Bonato,et al.  Toppling numbers of complete and random graphs , 2013, Discret. Math. Theor. Comput. Sci..

[11]  Jonathan D. Lee,et al.  New $\mathcal{F}$-Saturation Games on Directed Graphs , 2014, 1409.0565.