Abstract
AbstractLet be an integer, be the set of vertices of degree at least 2k in a graph G, and be the set of vertices of degree at most in G. In 1963, Dirac and Erdős proved that G contains k (vertex) disjoint cycles whenever . The main result of this article is that for , every graph G with containing at most t disjoint triangles and with contains k disjoint cycles. This yields that if and , then G contains k disjoint cycles. This generalizes the Corrádi–Hajnal Theorem, which states that every graph G with and contains k disjoint cycles.
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