Discussiones Mathematicae Graph Theory 32(1) (2012) 181-185
doi: 10.7151/dmgt.1596

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The first player wins the one-colour triangle avoidance game on 16 vertices

Przemysław Gordinowicz

Institute of Mathematics
Technical University of Lodz
Łódź, Poland

Paweł Prałat

Department of Mathematics
West Virginia University
Morgantown, WV 26506--6310, USA

Abstract

We consider the one-colour triangle avoidance game. Using a high performance computing network, we showed that the first player can win the game on 16 vertices.

Keywords: triangle avoidance game, combinatorial games

2010 Mathematics Subject Classification: 05C57, 05C35.

References

[1]S.C. Cater, F. Harary and R.W. Robinson, One-color triangle avoidance games, Congr. Numer. 153 (2001) 211--221.
[2]F. Harary, Achievement and avoidance games for graphs, Ann. Discrete Math. 13 (1982) 111--119.
[3]B.D. McKay, nauty Users Guide (Version 2.4),
http://cs.anu.edu.au/~bdm/nauty/.
[4]B.D. McKay, personal communication.
[5]P. Prałat, A note on the one-colour avoidance game on graphs, J. Combin. Math. and Combin. Comp. 75 (2010) 85--94.
[6]Á. Seress, On Hajnal's triangle-free game, Graphs and Combin. 8 (1992) 75--79, doi: 10.1007/BF01271710.
[7]D. Singmaster, Almost all partizan games are first person and almost all impartial games are maximal, J. Combin. Inform. System Sci. 7 (1982) 270--274.
[8]A UNIX script and programs written in C/C++ used to solve the problem,
http://www.math.wvu.edu/~pralat/index.php?page=publications.

Received 8 December 2010
Revised 7 March 2011
Accepted 8 March 2011