关于反凯库勒与$s$-限制匹配规避问题
On anti-Kekulé and $s$-restricted matching preclusion problems
AI总结：
本研究提出$s$-限制匹配规避数作为匹配规避数与反凯库勒数的统一推广，证明相关问题的NP完全性，给出正则图的计算充分条件，并确定了几类典型网络的对应数值。
摘要：
连通图$G$的反凯库勒数是指删除最少数量的边后，得到的连通子图不存在凯库勒结构（完美匹配）的边数。作为图$G$的（条件）匹配规避数与反凯库勒数的统一推广，我们引入图$G$的$s$-限制匹配规避数，定义为删除最少数量的边后，所得子图不存在完美匹配，且每个连通分量至少包含$s+1$个顶点的边数。本文首先证明条件匹配规避问题与反凯库勒问题均为NP完全问题，随后将该结果推广到$s$-限制匹配规避问题。此外，我们给出了计算正则图$s$-限制匹配规避数的若干充分条件。作为应用，确定了完全图、超立方体与超彼得森网络的$s$-限制匹配规避数。
英文摘要：
The anti-Kekulé number of a connected graph $G$ is the smallest number of edges whose deletion results in a connected subgraph having no Kekulé structures (perfect matchings). As a common generalization of (conditional) matching preclusion number and anti-Kekulé number of a graph $G$, we introduce $s$-restricted matching preclusion number of $G$ as the smallest number of edges whose deletion results in a subgraph without perfect matchings such that each component has at least $s+1$ vertices. In this paper, we first show that conditional matching preclusion problem and anti-Kekulé problem are NP-complete, respectively, then generalize this result to $s$-restricted matching preclusion problem. Moreover, we give some sufficient conditions to compute $s$-restricted matching preclusion numbers of regular graphs. As applications, $s$-restricted matching preclusion numbers of complete graphs, hypercubes and hyper Petersen networks are determined.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
