A degree and forbidden subgraph condition for a k-contractible edge

Abstract

An edge in a k-conected graph is said to be k-contractible if the contraction of it results in a k-connected graph. We say that k-connected graph G satis es “ degree-sum conditon ”if Σx2V (W)degG(x) 3k +2 holds for any connected subgraph W of G with 　｜W｜= 3. Let k be an integer such that k 5. We prove that if a k-connected graph with no K1+C4 satis es degree-sum condition, then it has a k-contractible edge.電気通信大学201