The Maximum Size of C4-Free Planar Graphs.

A planar graph is called C-4-free if it has no cycles of length four. Let f (n, C-4) denote the maximum size of a C-4-free planar graph with order n. In this paper, it is shown that f (n, C-4) = left perpendicular 15/7 (n-2)right perpendicular - mu for n >= 30, where mu, = 1 if n equivalent to 3(mod 7) or n = 32, 33,37, and mu = 0 otherwise.