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arXiv math/0609756math.CO
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图中匹配扩张的推广（II）

Generalization of matching extensions in graphs (II)

Zemin Jin, Huifang Yan, Qinglin Yu

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12 pages
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摘要：

Liu和Yu（Discrete Math.231（2001）311-320）提出了一个通用的框架，引入了$(n,k,d)$ -图来统一匹配不足、$n$ -因子临界性和$k$ -可扩展性的概念。设$G$是一个图，$n,k$和$d$是非负整数，使得$n+2k+d\leq |V(G)|-2$和$|V(G)|-n-d$是偶数.如果当从$G$中删除任何$n$顶点时，$G$的剩余子图$H$包含一个$k$ -匹配，并且每个这样的$k$ -匹配可以扩展为$H$中的一个缺陷- $d$匹配，则$G$称为$(n,k,d)$ -图.在\cite{Liu}中，给出了不同参数$n, k$和$d$的递归关系，并讨论了在$d = 0$情况下增加或删除边的影响.在本文中，我们继续在\cite{Liu}开始的研究，并获得新的递归结果$(n,k,d)$ -图在一般情况下$d \geq0$。

英文摘要：

Proposed as a general framework, Liu and Yu(Discrete Math. 231 (2001) 311-320) introduced $(n,k,d)$-graphs to unify the concepts of deficiency of matchings, $n$-factor-criticality and $k$-extendability. Let $G$ be a graph and let $n,k$ and $d$ be non-negative integers such that $n+2k+d\leq |V(G)|-2$ and $|V(G)|-n-d$ is even. If when deleting any $n$ vertices from $G$, the remaining subgraph $H$ of $G$ contains a $k$-matching and each such $k$- matching can be extended to a defect-$d$ matching in $H$, then $G$ is called an $(n,k,d)$-graph. In \cite{Liu}, the recursive relations for distinct parameters $n, k$ and $d$ were presented and the impact of adding or deleting an edge also was discussed for the case $d = 0$. In this paper, we continue the study begun in \cite{Liu} and obtain new recursive results for $(n,k,d)$-graphs in the general case $d \geq0$.

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。

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