Abstract
Let S denote the graph obtained from K4 by removing two edges which have an endvertex in common. Let k be an integer with k≥2. Let G be a graph with |V(G)|≥4k and σ2(G)≥|V(G)|/2+2k−1, and suppose that G contains k vertex-disjoint triangles. In the case where |V(G)|=4k+2, suppose further that G≅K4t+3∪K4k−4t−1 for any t with 0≤t≤k−1. Under these assumptions, we show that G contains k vertex-disjoint copies of S.
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