For a graph G of order n and a positive integer k,a k-weak cycle partition of G,called k-WCP,is a sequence of vertex disjoint subgraphs H_(1),H_(2),…,H_(k) of G with■_(i=1)^(k),where H_(i) is isomorphic to K_(1),K_(...For a graph G of order n and a positive integer k,a k-weak cycle partition of G,called k-WCP,is a sequence of vertex disjoint subgraphs H_(1),H_(2),…,H_(k) of G with■_(i=1)^(k),where H_(i) is isomorphic to K_(1),K_(2) or a cycle.Letσ_(2)(G)=min{d(x)+d(y):xy■E(G),x,y∈V(G)}.Hu and Li[Discrete Math.307(2007)]proved that if G is a graph of order n≥k+12 with a k-WCP andσ_(2)(G)≥2n+k-4/3,then G contains a k-WCP with at most one subgraph isomorphic to K_(2).In this paper,we generalize their result on the analogy of Fan-type condition that max{d(x),d(y)}≥2n+k-4/6 for each pair of nonadjacent vertices x,y∈V(G).展开更多
基金supported by the National Natural Science Foundation of China(No.11901268)The Fun-damental Research Funds for the Universities of Liaoning Province(No.LJ212410165065).
文摘For a graph G of order n and a positive integer k,a k-weak cycle partition of G,called k-WCP,is a sequence of vertex disjoint subgraphs H_(1),H_(2),…,H_(k) of G with■_(i=1)^(k),where H_(i) is isomorphic to K_(1),K_(2) or a cycle.Letσ_(2)(G)=min{d(x)+d(y):xy■E(G),x,y∈V(G)}.Hu and Li[Discrete Math.307(2007)]proved that if G is a graph of order n≥k+12 with a k-WCP andσ_(2)(G)≥2n+k-4/3,then G contains a k-WCP with at most one subgraph isomorphic to K_(2).In this paper,we generalize their result on the analogy of Fan-type condition that max{d(x),d(y)}≥2n+k-4/6 for each pair of nonadjacent vertices x,y∈V(G).
