Optimal strong parity edge-coloring of complete graphs

A parity walk in an edge-coloring of a graph is a walk along which each color is used an even number of times. Let p(G) be the least number of colors in an edge-coloring of G having no parity path (a parity edge-coloring). Let p(G) be the least number of colors in an edge-coloring of G having no open parity walk (a strong parity edge-coloring). Always p(G) p(G) (G). We prove that p(Kn) = 2 lg n -1 for all n. The optimal strong parity edge-coloring of Kn is unique when n is a power of 2, and the optimal colorings are completely described for all n.

• Type: Journal
• Year: 2008
• Where: COMBINATORICA
• Authors: David P. Bunde, Kevin Milans, Douglas B. West, Hehui Wu
• Keywords: COMBINATORICA 2008, Parity Edge-coloring, Parity Path, Parity Walk