A Symmetric Strategy in Graph Avoidance Games
Abstract
In the graph avoidance game two players alternatingly color edges of a graph G in red and in blue respectively. The player who first creates a monochromatic subgraph isomorphic to a forbidden graph F loses. A symmetric strategy of the second player ensures that, independently of the first player's strategy, the blue and the red subgraph are isomorphic after every round of the game. We address the class of those graphs G that admit a symmetric strategy for all F and discuss relevant graphtheoretic and complexity issues. We also show examples when, though a symmetric strategy on G generally does not exist, it is still available for a particular F.
 Publication:

arXiv eprints
 Pub Date:
 October 2001
 arXiv:
 arXiv:cs/0110049
 Bibcode:
 2001cs.......10049H
 Keywords:

 Computer Science  Discrete Mathematics;
 Computer Science  Computational Complexity;
 F.1.3;
 G.2.1;
 G.2.2
 EPrint:
 14 pages, 6 figures