Abstract
We prove a variant of a theorem of Corrádi and Hajnal (1963) [4] which says that if a graph G has at least 3k vertices and its minimum degree is at least 2k, then G contains k vertex-disjoint cycles. Specifically, our main result is the following. For any positive integer k, there is a constant ck such that if G is a graph with at least ck vertices and the minimum degree of G is at least 2k, then (i) G contains k vertex-disjoint even cycles, or (ii) (2k−1)K1∨pK2⊂G⊂K2k−1∨pK2 (p⩾k⩾2), or (iii) k=1 and each block of G is either a K2 or an odd cycle.
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