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- W2073362670 abstract "We study a competitive optimization version of α′(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 αg′(G) and αˆg′(G), respectively. We show that always |αg′(G)−αˆg′(G)|≤1. We obtain a sufficient condition for αg′(G)=α′(G). Always αg′(G)≥23α′(G), with equality for many split graphs, while αg′(G)≥34α′(G) when G is a forest. Whenever G is a 3-regular n-vertex connected graph, αg′(G)≥n/3, and such graphs exist with αg′(G)<7n/18. For an n-vertex path or cycle, the value is roughly n/7." @default.
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- W2073362670 date "2013-09-01" @default.
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- W2073362670 title "Game matching number of graphs" @default.
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- W2073362670 doi "https://doi.org/10.1016/j.dam.2013.03.010" @default.
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