On the structure of extremal graphs of high girth

  title={On the structure of extremal graphs of high girth},
  author={Felix Lazebnik and Ping Wang},
  journal={Journal of Graph Theory},
Let n ≥ 3 be a positive integer, and let G be a simple graph of order v containing no cycles of length smaller than n + 1 and having the greatest possible number of edges (an extremal graph). Does G contain an n + 1–cycle? In this paper we establish some properties of extremal graphs and present several results where this question is answered affirmatively. For example, this is always the case for (i) v ≥ 8 and n = 5, or (ii) when v is large compared to n: v ≥ 2a2+a+1na, where a = n − 3 − n−2 4… CONTINUE READING