Density of Gallai Multigraphs

Colton Magnant

Abstract


Diwan and Mubayi asked how many edges of each color could be included in a $3$-edge-colored multigraph containing no rainbow triangle.  We answer this question under the modest assumption that the multigraphs in question contain at least one edge between every pair of vertices.  We also conjecture that this assumption is, in fact, without loss of generality.

Keywords


rainbow triangle, Gallai coloring, multigraph

Full Text: PDF