For a graph G,letμ(G)=min{max{d(x),d(y)}:x≠y,xy∉E(G),x,y∈V(G)}if G is non-complete,otherwise,μ(G)=+∞.For a given positive number s,we call that a graph G satisfies Fan-type conditions ifμ(G)≥s.Supposeμ(G)≥s,t...For a graph G,letμ(G)=min{max{d(x),d(y)}:x≠y,xy∉E(G),x,y∈V(G)}if G is non-complete,otherwise,μ(G)=+∞.For a given positive number s,we call that a graph G satisfies Fan-type conditions ifμ(G)≥s.Supposeμ(G)≥s,then a vertex v is called a small vertex if the degree of v in G is less than s.In this paper,we prove that for a forest F with m edges,if G is a graph of order n≥|F|andμ(G)≥m with at most max{n−2m,0}small vertices,then G contains a copy of F.We also give examples to illustrate both the bounds in our result are best possible.展开更多
基金the National Natural Science Foundation of China(No.11901268)Research Fund of the Doctoral Program of Liaoning Normal University(No.2021BSL011).
文摘For a graph G,letμ(G)=min{max{d(x),d(y)}:x≠y,xy∉E(G),x,y∈V(G)}if G is non-complete,otherwise,μ(G)=+∞.For a given positive number s,we call that a graph G satisfies Fan-type conditions ifμ(G)≥s.Supposeμ(G)≥s,then a vertex v is called a small vertex if the degree of v in G is less than s.In this paper,we prove that for a forest F with m edges,if G is a graph of order n≥|F|andμ(G)≥m with at most max{n−2m,0}small vertices,then G contains a copy of F.We also give examples to illustrate both the bounds in our result are best possible.
