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| 1 | EDGE COVERING COLORING AND FRACTIONAL EDGE COVERING COLORING显示文摘Abstract. Let G be a graph with edge set E(G). S E(G) is called an edge cover of G ifevery vertex of G is an end vertex of some edges in S. The edge covering chromatic numberof a graph G, denoted by Xc(G) is the maximum size of a partition of E(G) into edgecovers of G. It is known that for any graph G with minimum degree δ,δ- 1 The fractional edge covering chromatic number of a graph G, denoted by Xcf(G), is thefractional matching number of the edge covering hypergraph H of G whose vertices arethe edges of G and whose hyperedges the edge covers of G. In this paper, we studythe relation between X’c(G) and δ for any graph G, and give a new simple proof of theinequalities δ - 1 ≤ X’c(G) ≤ δ by the technique of graph coloring. For any graph G, wegive an exact formula of X’cf(G), that is,where A(G)=minand the minimum is taken over all noempty subsets S of V(G) and C[S] is the set of edgesthat have at least one end in S. | MIAOLianying LIUGuizhen | 2002 | Journal of Systems Science & Complexity2002，15，2： | 10 |
| 2 | The connectivities of adjacent treegraphs显示文摘 | LiuGuizhen | 1987 | Acta Mathematics Applied Sinica1987，3，4： | 1 |
| 3 | Onedgecoloringsof1-planargraphswithoutadjacenttriangles显示文摘 | ZHANGXin LIUGuizhen | 2012 | InformationProcessingLetters2012，112，： | 1 |
| 4 | On(g,f)coveredgraph显示文摘 | LIUGuizhen | 1988 | ActaMathematiScienta1988，8，2： | 1 |
| 5 | (g,f)factorsandfactorizationsofgraphs显示文摘 | LIUGuizhen | 1994 | ActaMathematiScienta1994，37，2： | 1 |
| 6 | On(g,f)uniformgraphs显示文摘 | LIUGuizhen LIUYan | 2005 | ActaApplMathSinica2005，21，1： | 1 |
| 7 | Acyclicedgechromaticnumberofouterplanargraphs显示文摘 | HOUJianfeng WUJianliang LIUGuizhen etal | 2010 | JGraphTheory2010，64，： | 1 |
| 8 | (g,f)-FACTORS WITH SPECIAL PROPERTIES IN BIPARTITE (mg,mf)-GRAPHS显示文摘Let G be a bipartite graph and g and f be two positive integer-valued functions defined on vertex set V(G) of G such that g(x)≤f(x).In this paper,some sufficient conditions related to the connectivity and edge-connectivity for a bipartite (mg,mf)-graph to have a (g,f)-factor with special properties are obtained and some previous results are generalized.Furthermore,the new results are proved to be the best possible. | BianQiuju LiuGuizhen | 2004 | Applied Mathematics(A Journal of Chinese Universities)2004，19，2： | 0 |
| 9 | VERTEX-DISJOINT QUADRILATERALS IN BIPARTITE GRAPHS显示文摘H.Wang considered the minimum degrees condition that G has large vertexdisjoint cycles in bipartite graphs.Motivated by this,we consider the small vertex-disjoint cycles in bipartite graphs in this paper.We prove the following result:Let m≥3,n≥2 and k≥1 be three integers.Let G=(V1,V2;E)be a bipartite graph with |V1|=|V2|=n≥2k+1.If the minimum degree δ(G)≥k+1and x∈V(C)^∑d(x)≥m(n+1)+1 for any cycle C of G with length 2m,then Gcontains k vertex-disjoint cycles of length 4.Moreover,the degrees condition is sharp. | YANJin LIUGuizhen | 2004 | Journal of Systems Science & Complexity2004，17，4： | 0 |
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