标题： $(n,k)$可扩展图的曲面嵌入 显示英文标题

标题： Surface embedding of $(n,k)$-extendable graphs

摘要： 本文研究的是可匹配扩展图的表面嵌入。 扩展完美匹配理论有两个方向，即匹配扩展性和因子临界性。 在解决Plummer提出的问题时，Dean（The matching extendability of surfaces, J. Combin. Theory Ser. B 54 (1992), 133--141）建立了关于最小数$k= \mu (\Sigma) $的迷人公式，使得每个$\Sigma$-可嵌入图都不是$k$-扩展的。 Su和Zhang，Plummer和Zha找到了最小数$n=\rho(\Sigma)$，使得每个$\Sigma$-可嵌入图都不是$n$-因子临界的。 基于$(n,k)$-图的概念，该概念将这两个参数联系起来，我们找到了最小数$k=\mu(n,\Sigma)$的公式，使得每个$\Sigma$-可嵌入图都不是$(n,k)$-图。 为了处理这个双参数问题，我们考虑其对偶问题，并反过来发现$\mu(n,\Sigma)$。 同样的方法适用于重新发现数$\rho(\Sigma)$的公式。 显示英文摘要

摘要： This paper is concerned with the surface embedding of matching extendable graphs. There are two directions extending the theory of perfect matchings, that is, matching extendability and factor-criticality. In solving a problem posed by Plummer, Dean (The matching extendability of surfaces, J. Combin. Theory Ser. B 54 (1992), 133--141) established the fascinating formula for the minimum number $k= \mu (\Sigma) $ such that every $\Sigma$-embeddable graph is not $k$-extendable. Su and Zhang, Plummer and Zha found the minimum number $n=\rho(\Sigma)$ such that every $\Sigma$-embeddable graph is not $n$-factor-critical. Based on the notion of $(n,k)$-graphs which associates these two parameters, we found the formula for the minimum number $k=\mu(n,\Sigma)$ such that every $\Sigma$-embeddable graph is not an $(n,k)$-graph. To access this two-parameter-problem, we consider its dual problem and find out $\mu(n,\Sigma)$ conversely. The same approach works for rediscovering the formula of the number $\rho(\Sigma)$.