A minimax result for perfect matchings of a polyomino graph
Authors: 
Xiangqian Zhou and Heping ZhangAuthors Info & Claims
Xiangqian Zhou and Heping ZhangAuthors Info & ClaimsPages 165 - 171
Abstract
Let G be a plane bipartite graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M such that S is not contained by other perfect matchings of G . The minimum cardinality of forcing sets of M is called the forcing number of M, denoted by f ( G, M ) . Pachter and Kim established a minimax result: for any perfect matching M of G, f ( G, M ) is equal to the maximum number of disjoint M -alternating cycles in G . For a polyomino graph H, we show that for every perfect matching M of H with the maximum or second maximum forcing number, f ( H, M ) is equal to the maximum number of disjoint M -alternating squares in H . This minimax result does not hold in general for other perfect matchings of H with smaller forcing number.
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Published: 19 June 2016
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