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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...
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