Characterization of edge-colored complete graphs with properly colored Hamilton paths

An edge-colored graph H is properly colored if no two adjacent edges of H have the same color. In 1997, J. Bang-Jensen and G. Gutin conjectured that an edgecolored complete graph G has a properly colored Hamilton path if and only if G has a spanning subgraph consisting of a properly colored path C0 and a (possibly empty) collection of properly colored cycles C1, C2, . . . , Cd such that V (Ci) V (Cj) = provided 0 i < j d. We prove this conjecture.

• Type: Journal
• Year: 2006
• Where: JGT
• Authors: Jinfeng Feng, Hans-Erik Giesen, Yubao Guo, Gregory Gutin, Tommy R. Jensen, Arash Rafiey
• Keywords: Adjacent Edges, Edge-colored Graph, Edgecolored Complete Graph, JGT 2006