Cycles and paths in edge-colored graphs with given degrees

Sufficient degree conditions for the existence of properly edge-colored cycles and paths in edge-colored graphs, multigraphs and random graphs are inverstigated. In particular, we prove that an edgecolored multigraph of order n on at least three colors and with minimum colored degree greater than or equal to n+1 2 has properly edge-colored cycles of all possible lengths, including hamiltonian cycles. Longest properly edge-colored paths and hamiltonian paths between given vertices are considered as well.

• Type: Journal
• Year: 2010
• Where: JGT
• Authors: A. Abouelaoualim, Kinkar Chandra Das, Wenceslas Fernandez de la Vega, Marek Karpinski, Yannis Manoussakis, Carlos A. J. Martinhon, Rachid Saad
• Keywords: Hamiltonian Paths, JGT 2010, Minimum Colored Degree, Sufficient Degree Conditions