论文标题
一些新型的最小值结果，以实现六角形系统的完美匹配
Some novel minimax results for perfect matchings of hexagonal systems
论文作者
论文摘要
$ g $的完美匹配$ m $的反施加数量是$ g $的最小边缘数量，其删除会导致子图，并带有独特的完美匹配$ m $，用$ af（g，m）$表示。当$ g $是飞机的两分图时，Lei等人。建立了一个最小值结果：对于任何完美匹配的$ m $ $ g $，$ af（g，m）$等于$ m $的最大数量，即$ g $的$ m $偏置周期，任何两个都不相交或仅在$ m $中的边缘相交；对于六边形系统，最大抗强化数等于薯条数。在本文中，我们表明，对于每一个完美匹配的六角形系统的$ m $ $ h $，具有最大的反施加数字或减去一个，$ af（h，m）$等于$ m $ m $ a $ hexagons $ h $的数量。此外，我们表明，六边形系统$ h $在$ af（h，m）$的情况下具有三苯基元素为良好的子图，总是等于$ m $ $ m $的六角形$ h $的$ h $ $ h $，对于每个完美匹配的$ m $ $ h $。
The anti-forcing number of a perfect matching $M$ of a graph $G$ is the minimum number of edges of $G$ whose deletion results in a subgraph with a unique perfect matching $M$, denoted by $af(G,M)$. When $G$ is a plane bipartite graph, Lei et al. established a minimax result: For any perfect matching $M$ of $G$, $af(G,M)$ equals the maximum number of $M$-alternating cycles of $G$ where any two either are disjoint or intersect only at edges in $M$; For a hexagonal system, the maximum anti-forcing number equals the fries number. In this paper we show that for every perfect matching $M$ of a hexagonal system $H$ with the maximum anti-forcing number or minus one, $af(H,M)$ equals the number of $M$-alternating hexagons of $H$. Further we show that a hexagonal system $H$ has a triphenylene as nice subgraph if and only $af(H,M)$ always equals the number of $M$-alternating hexagons of $H$ for every perfect matching $M$ of $H$.
