On maximal triangle-free graphs

A triangle-free graph is maximal if adding any edge will create a triangle. The minimal number of edges of a maximal triangle-free graph on n vertices having maximal degree at most D is denoted by F(n, D). We determine the value of lim_n-∞ F(n, cn)/n for 2/5 < c < 1/2. This investigation continues work done by Z. Füredi and Á. Seress. Our result is contrary to a conjecture of theirs.