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- W913771037 abstract "Let G be a graph with edge set E(G).S E（G)is called an edge cover of G if every vertex of G is an end vertex of some edges in S.The edge covering chromatic number of a graph G,denoted by Xc(G),is the maximum size of a partition of E(G) into edge covers of G.It is known that for any graph G with minimum degree δ,δ-1≤Xc(G)≤δ.The fractional edge covering chromatic number of a graph G,denoted by Xcf(G),is the fractional matiching number of the edge covering hypergraph H of G whose vertices are the edges of G and whose hypereges the edge covers of G.In this paper,we study the relation between Xc(G) and δfor any graph G,and give a new simple proof of the inequalities δ-1≤Xc(G)≤δ by the technique of graph coloring.For any graph G,we give an exact formula o Xcf(G),that is,Xcf(G)=min{δ,λ(G)},where λ(G)=minCS/S/2 and the minimum is taken over all noempty subsets S of V(G) and C[S] is the set of edges that have at least one end in S.δ" @default.
- W913771037 created "2016-06-24" @default.
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- W913771037 date "2002-01-01" @default.
- W913771037 modified "2023-09-26" @default.
- W913771037 title "EDGE COVERING COLORING AND FRACTIONAL EDGE COVERING COLORING" @default.
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