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Discussiones Mathematicae Graph Theory 32(1) (2012)
181-185
DOI: https://doi.org/10.7151/dmgt.1596
The first player wins the one-colour triangle avoidance game on 16 vertices
| Przemysław Gordinowicz
Institute of Mathematics | Paweł Prałat
Department of Mathematics |
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. |
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| [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
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