Edges In Graphs With Large Girth
Title - Alternative
Several upper bounds are given for the maximum number of edges e possible in a graph depending upon its order p, girth g and, in certain cases, minimum degree delta. In particular, one upper bound has an asymptotic order of p1+2/(g-1) when g is odd. A corollary of our final result is that g less-than-or-equal-to 2 + 2 log(k) (p/4) when k = [e/p] greater-than-or-equal-to 2. Asymptotic and numerical comparisons are also presented.
Graphs and Combinatorics
Dutton, R D. and Brigham, R C., "Edges In Graphs With Large Girth" (1991). Faculty Bibliography. 1270.