The edge domination number $\gamma_e(G)$ of a graph $G$ is the minimum size of a maximal matching in $G$. It is well known that this parameter is computationally very hard, and several approximation algorithms and heuristics have been studied. In the present paper, we provide best possible upper bounds on $\gamma_e(G)$ for regular and non-regular graphs $G$ in terms of their order and maximum degree. Furthermore, we discuss algorithmic consequences of our results and their constructive proofs.

中文翻译：

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正则图中最小最大匹配的边界和逼近

图$G$的边支配数$\gamma_e(G)$是$G$中最大匹配的最小尺寸。众所周知，该参数在计算上非常困难，并且已经研究了几种近似算法和启发式方法。在本文中，我们为规则和非规则图 $G$ 的顺序和最大度数提供了 $\gamma_e(G)$ 的最佳可能上限。此外，我们讨论了我们的结果及其构造性证明的算法后果。