Perfect Set of Euler Tours of Kp,p,p

Abstract

Bermond conjectured that if G is Hamilton cycle decomposable, then L(G), the line graph of G, is Hamilton cycle decomposable. In this paper, we construct a perfect set of Euler tours for the complete tripartite graph Kp,p,p for any prime p and hence prove Bermond’s conjecture for G = Kp,p,p.

Keywords

• compatible euler tour
• line graph
• hamilton cycle decomposition