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Graphs and Combinatorics

, Volume 28, Issue 6, pp 901–905 | Cite as

A Note on Heterochromatic C 4 in Edge-Colored Triangle-Free Graphs

  • Guanghui Wang
  • Hao Li
  • Yan Zhu
  • Guizhen LiuEmail author
Original Paper

Abstract

Let G be an edge-colored graph. A heterochromatic cycle of G is a cycle in which any pair of edges have distinct colors. Let d c (v), named the color degree of a vertex v, be defined as the maximum number of edges incident with v, that have distinct colors. In this paper, we prove that if G is an edge-colored triangle-free graph of order n ≥ 9 and \({d^c(v) \geq \frac{(3-\sqrt{5})n}{2}+1}\) for each vertex v of G, G has a heterochromatic C 4.

Keywords

Heterochromatic cycle Color neighborhood Color degree 

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Copyright information

© Springer 2011

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina
  2. 2.Laboratoire de Recherche en InformatiqueUMR 8623, C.N.R.S.-Université de Paris-sudOrsay cedexFrance
  3. 3.Department of MathematicsEast China University of Science and TechnologyShanghaiChina

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