\magnification=1440
\font\bigtenrm=cmr10 scaled\magstep4
Abstract for James B. Shearer, The Independence Number of Dense Graphs with Large Odd Girth

Let $G$ be a graph with $n$ vertices and odd girth
$2k+3$.   Let the degree of a vertex $v$ of $G$ be $d_1 (v)$.
Let $\alpha (G)$ be the independence number of $G$.
Then we show $\alpha (G) \geq 2^{-\left({{k-1}\over {k}}\right)} \left[
\displaystyle{\sum_{v\in G}} d_1
(v)^{{{1}\over {k-1}}} \right]^{(k-1)/k}$.  This improves and simplifies
results proven by Denley.

\bye

.
