Gives a new lower bound for cycle lengths in graphs with large girth, highlighting implications for cycle structure in various graph types.
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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Fujisawa et al. (2014) studied this question.
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