Vertex-disjoint quadrilaterals in graphs

AbstractLet k be a positive integer and G a graph of order n. In (Discrete Math. 203 (1999) 229), we proved that if n=4k and δ(G)⩾2k then G contains k-1 vertex-disjoint quadrilaterals. In this paper, we investigate vertex-disjoint quadrilaterals in G with n≢0(mod4), and we have found the best minimum degree condition δ(G)⩾⌈12n⌉ such that G contains ⌊14n⌋ vertex-disjoint quadrilaterals. As a result of our method, we have improved our previous result as follows: If n=4k and δ(G)⩾2k-1 then G contains k-1 vertex-disjoint quadrilaterals