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Cycles and paths in edge-colored graphs with given degrees

✍ Scribed by A. Abouelaoualim,; K. Ch. Das; W. Fernandez de la Vega; M. Karpinski; Y. Manoussakis; C. A. Martinhon; R. Saad

Publisher: John Wiley and Sons
Year: 2009
Tongue: English
Weight: 203 KB
Volume: 64
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20440

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✦ Synopsis

Abstract

Sufficient degree conditions for the existence of properly edge‐colored cycles and paths in edge‐colored graphs, multigraphs and random graphs are investigated. In particular, we prove that an edge‐colored 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. © 2009 Wiley Periodicals, Inc. J Graph Theory 64: 63–86, 2010

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