关于(ξ,1)-临界图与上可嵌入性

On(ξ,1)-Critical Graphs and Upper Embeddability

设G为连通图,且(ξG)=k≥1,若对G中任意边e,有ξ(G\e)=k-1,则称G为(ξ,k)-临界图.利用ξ-1-临界图的上可嵌入性,通过研究ξ-1-临界图的加重边、点扩张、圈扩张的ξ-1-临界性,得到了新的上可嵌入图,从而丰富了上可嵌入图的种类和求法.

Let G be a connected graph with ξ(G)=k≥1.If ξ(G\e)=k-1,G is called to be a(ξ,1)-critical graph.This paper gives the upper embeddability of the ξ-1-critical graphs,and shows that extension of a vertex and extension of a cycle dose not change the ξ-1-cirtical graphs.The new upper embeddable graphs are obtained,enriching the kind and seeking methods.