Abstract
The edge domination number γe(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 γe(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.
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