# Game matching number of graphs

@article{Cranston2013GameMN,
title={Game matching number of graphs},
author={Daniel W. Cranston and Bill Kinnersley and O Suil and Douglas B. West},
journal={Discret. Appl. Math.},
year={2013},
volume={161},
pages={1828-1836}
}
We study a competitive optimization version of @a^'(G), the maximum size of a matching in a graph G. Players alternate adding edges of G to a matching until it becomes a maximal matching. One player (Max) wants the final matching to be large; the other (Min) wants it to be small. The resulting sizes under optimal play when Max or Min starts are denoted @a"g^'(G) and @a@?"g^'(G), respectively. We show that always |@a"g^'(G)-@a@?"g^'(G)|@?1. We obtain a sufficient condition for @a"g^'(G)=@a^'(G…

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