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Consecutive Edge-Colorings of Generalized θ-Graphs

  • Yongqiang Zhao
  • Gerard J. Chang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7033)

Abstract

A proper edge-coloring of a graph G using positive integers as colors is said to be a consecutive edge-coloring if for each vertex the colors of edges incident form an interval of integers. Recently, Feng and Huang studied the consecutive edge-coloring of generalized θ-graphs. A generalized θ-graph is a graph consisting of m internal disjoint (u,v)-paths, where 2 ≤ m < ∞. This paper investigates a problem provided by Feng and Huang, and gives a positive answer to the problem, except two cases are left.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Yongqiang Zhao
    • 1
  • Gerard J. Chang
    • 2
    • 3
    • 4
  1. 1.Department of MathematicsShijiazhuang UniversityShijiazhuangP.R. China
  2. 2.Department of MathematicsNational Taiwan UniversityTaipeiTaiwan
  3. 3.Institute for Mathematical SciencesNational Taiwan UniversityTaipeiTaiwan
  4. 4.National Center for Theoretical SciencesTaipei OfficeTaiwan

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