Covering a graph with cycles

Let k and n be two integers such that k ≥ 0 and n ≥ 3( k + 1). Let G be a graph of order n with minimum degree at least ⌈( n + k )/2⌉. Then G contains k + 1 independent cycles covering all the vertices of G such that k of them are triangles. © 1995, John Wiley & Sons, Inc.