Abstract
AbstractThe set of different cycle lengths of a graph G is denoted by C(G). We study how the distribution of C(G) depends on the minimum degree of G. We prove two results indicating that C(G) is dense in some sense. These results lead to the solution of a conjecture of Erdös and Hajnal stating that for suitable positive constants a, b the following holds: magnified image where δ(G) denotes the minimum degree of G.
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