Caro, Davila, and Pepper (arXiv:1909.09093) recently proved $\delta(G) \alpha(G)\leq \Delta(G) \mu(G)$ for every graph $G$ with minimum degree $\delta(G)$, maximum degree $\Delta(G)$, independence number $\alpha(G)$, and matching number $\mu(G)$. Answering some problems they posed, we characterize the extremal graphs for $\delta(G)<\Delta(G)$ as well as for $\delta(G)=\Delta(G)=3$.

中文翻译：

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具有相等独立数和匹配数的三次图

Caro、Davila 和 Pepper (arXiv:1909.09093) 最近证明了 $\delta(G) \alpha(G)\leq \Delta(G) \mu(G)$ 对于每个具有最小度数 $\delta( G)$、最大度数$\Delta(G)$、独立数$\alpha(G)$、匹配数$\mu(G)$。回答他们提出的一些问题，我们表征了 $\delta(G)<\Delta(G)$ 以及 $\delta(G)=\Delta(G)=3$ 的极值图。