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

  • Authors:

  • Jinfeng Feng;Hans-Erik Giesen;Yubao Guo;Gregory Gutin;Tommy Jensen;Arash Rafiey

  • Affiliations:

  • Lehrstuhl C Fuer Mathematik, RWTH Aachen University, 52056 Aachen, Germany;Lehrstuhl C Fuer Mathematik, RWTH Aachen University, 52056 Aachen, Germany;Lehrstuhl C Fuer Mathematik, RWTH Aachen University, 52056 Aachen, Germany;Department of Computer Science, Royal Holloway, University Of London, Egham, Surrey TW20 0EX, UK;Institut fuer Mathematik, Universitat Klagenfurt, Universitatsstrasse 65-67, 9020 Klagenfurt, Austria;Department of Computer Science, Royal Holloway, University Of London, Egham, Surrey TW20 0EX, UK

  • Venue:
  • Journal of Graph Theory
  • Year:
  • 2006

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Abstract

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 edge-colored 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 $V (C_i) \cap {V(C}_j) =\emptyset$ provided $0 \le i