The STP Number and the Embeddablity of A Graph
LU Chang-qing, Han Ren · Journal of Luoyang University · 2005
The STP number is the maximum edges-disjoint spanning tree in G,denoted σ(G).In this paper, we invesgate that the relations between the STP number and the embed and the embeddablity of a graph. We obtain that ω(G)p_0(2+b(G-E_0)p_0-σ(G)),where p_0=c(G-E_0)-1, c(G-E_0)denotes the components of G-E_0, b(G-E_0) is the components of G-E_0 with odd Betti number. As an appliation, we discuss the upper embeddablity of the graph G~3.