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Relations between the domination parameters and the chromatic index of a graph. (English) Zbl 1194.05119

Summary: We show upper bounds for the sum and the product of the lower domination parameters and the chromatic index of a graph. We also present some families of graphs for which these upper bounds are achieved. Next, we give a lower bound for the sum of the upper domination parameters and the chromatic index. This lower bound is a function of the number of vertices of a graph and a new graph parameter which is defined here. In this case we also characterize graphs for which a respective equality holds.

MSC:

05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C15 Coloring of graphs and hypergraphs
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