Bounds for graphs of given girth and generalized polygons

• Published in: Algebra and Discrete Mathematics
• Date: 2002
• Main Authors: Benkherouf, L., Ustimenko, V.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2002
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/154677
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Bounds for graphs of given girth and generalized polygons / L. Benkherouf, V. Ustimenko // Algebra and Discrete Mathematics. — 2002. — Vol. 1, № 1. — С. 1–18. — Бібліогр.: 26 назв. — англ.

In this paper we present a bound for bipartite graphs with average bidegrees η and ξ satisfying the inequality η ≥ ξ α, α ≥ 1. This bound turns out to be the sharpest existing bound. Sizes of known families of finite generalized polygons are exactly on that bound. Finally, we present lower bound...