aSchool of Information Technology, Jiangxi University of Finance, Nanchang 330013, PR China
Abstract:
Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ2(G)n+k-1. Let v1,…,vk be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C1,…,Ck with viV(Ci) for all 1ik.Then G has k vertex-disjoint cycles such that
(i) for all 1ik.
(ii) , and
(iii) At least k-1 of the k cycles are triangles.
The condition of degree sum σ2(G)n+k-1 is sharp.
Keywords: Degree sum condition; Independent vertices; Vertex-disjoint cycles