论文标题
平等匹配数和独立号码的常规图
Regular graphs with equal matching number and independence number
论文作者
论文摘要
令$ r \ geq 3 $为整数，$ g $为图。令$δ（g），δ（g）$，$α（g）$和$μ（g）$分别表示$ g $的最低度，最高度，独立数和匹配数。最近，Caro，Davila和Pepper证明了$δ（g）α（g）\leqΔ（g）μ（g）$。 Mohr和Rautenbach表征了非规范图和3个规则图的极端图。在本说明中，我们表征了Gallai-Edmonds结构定理的所有$ r $ ro $等级图的极端图，该图表扩展了Mohr和Rautenbach的结果。
Let $r\geq 3$ be an integer and $G$ be a graph. Let $δ(G), Δ(G)$, $α(G)$ and $μ(G)$ denotes minimum degree, maximum degree, independence number and matching number of $G$, respectively. Recently, Caro, Davila and Pepper proved $δ(G)α(G)\leq Δ(G)μ(G)$. Mohr and Rautenbach characterized the extremal graphs for non-regular graphs and 3-regular graphs. In this note, we characterize the extremal graphs for all $r$-regular graphs in term of Gallai-Edmonds Structure Theorem, which extends Mohr and Rautenbach's result.
