Degree-Sum Conditions for Graphs to Have 2-Factors with Cycles Through Specified Vertices
Toshinori Sakai · SUT Journal of Mathematics · 2002
Let k≥2 and n≥1 be integers, let G be a graph of order n with minimum degree at least k + 1. Let υ1,υ2,…,υk be k distinct vertices of G, and suppose that there exist k vertex disjoint cycles C1,…,Ck in G such that υi∈V(Ci) for each 1≤i≤k. Suppose further that the minimum value of the sum of the degrees of two nonadjacent distinct vertices is greater than or equal to n+k−43. Under these assumptions, we show that there is a 2-factor of G with k cycles D1,D2,…,Dk such that υi∈V(Di) for each 1≤i≤k.