Abstract
In this paper we give a lower bound of the circumference of a graph in terms of girth and the number of edges. It is shown that a graph of girth at least g≥4 with n vertices and at least m≥n edges contains a cycle of length at least (g− 2)m/(n − 2). In particular, for the case g = 4, an analogous result for 2-edge-connected weighted graphs is given. Moreover, the extremal case is characterized in both results.
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