On edge covering colorings of graphs |
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Authors: | Xia Zhang Guizhen Liu |
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Affiliation: | a Department of Mathematics, Shandong Normal University, Jinan, Shandong 250014, PR China b School of Mathematics, Shandong University, Jinan, Shandong 250100, PR China |
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Abstract: | An edge covering coloring of a graph G is an edge-coloring of G such that each color appears at each vertex at least one time. The maximum integer k such that G has an edge covering coloring with k colors is called the edge covering chromatic index of G and denoted by . It is known that for any graph G with minimum degree δ(G), it holds that . Based on the subgraph of G induced by the vertices of minimum degree, we find a new sufficient condition for a graph G to satisfy . This result substantially extends a result of Wang et al. in 2006. |
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Keywords: | Combinatorial problems Edge-coloring Graph Edge covering coloring Edge covering chromatic index |
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