ON SWELL-COLORED COMPLETE GRAPHS
C. WARD and S. SZABO
Abstract.
An edge-colored graph is said to be swell-colored if each triangle contains exactly 1 or 3 colors but never 2 colors and if the graph contains more than one color. It is shown that a swell-colored complete graph with n vertices contains at least $ \sqrt n + 1 $ colors. The complete graph with $n^2$ vertices has a swell coloring using $n + 1$ colors if and only if there exists a finite affine plane of order $n$.
Compressed Postscript 
