Disjoint triangles and quadrilaterals in a graph

Let G be a simple graph of order n and s and k   be two positive integers. Brandt et al. obtained the following result: If s⩽ks⩽k, n⩾3s+4(k-s)n⩾3s+4(k-s) and σ2(G)⩾n+sσ2(G)⩾n+s, then G contains k   disjoint cycles C1,…,CkC1,…,Ck satisfying |Ci|=3|Ci|=3 for 1⩽i⩽s1⩽i⩽s and |Ci|⩽4|Ci|⩽4 for s