## On extremal bipartite graphs with high girth

- Pedro García-Vázquez, Camino Balbuena, Xavier Marcote, Juan Carlos Valenzuela
- Electronic Notes in Discrete Mathematics
- 2006

Highly Influenced

@article{Lazebnik1997OnTS, title={On the structure of extremal graphs of high girth}, author={Felix Lazebnik and Ping Wang}, journal={Journal of Graph Theory}, year={1997}, volume={26}, pages={147-153} }

- Published 1997 in Journal of Graph Theory
DOI:10.1002/(SICI)1097-0118(199711)26:3%3C147::AID-JGT5%3E3.0.CO;2-R

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