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Edge domatic numbers of complete $$n$$-partite graphs. (English) Zbl 0819.05036
Authors’ abstract: An edge dominating set of a graph is a set of edges $$D$$ such that every edge not in $$D$$ is adjacent to an edge in $$D$$. An edge domatic partition of a graph $$G= (V, E)$$ is a collection of pairwise disjoint edge dominating sets of $$G$$ whose union is $$E$$. The maximum size of an edge domatic partition of $$G$$ is called the edge domatic number of $$G$$. In this paper we study the edge domatic numbers of complete $$n$$- partite graphs. In particular, we give exact values for the edge domatic numbers of complete 3-partite graphs and balanced complete $$n$$-partite graphs with odd $$n$$.

MSC:
 05C35 Extremal problems in graph theory
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References:
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