Journal of Combinatorial Optimization

, Volume 20, Issue 4, pp 429–442 | Cite as

On the max-weight edge coloring problem

  • Giorgio Lucarelli
  • Ioannis Milis
  • Vangelis T. Paschos


We study the following generalization of the classical edge coloring problem: Given a weighted graph, find a partition of its edges into matchings (colors), each one of weight equal to the maximum weight of its edges, so that the total weight of the partition is minimized. We explore the frontier between polynomial and NP-hard variants of the problem, with respect to the class of the underlying graph, as well as the approximability of NP-hard variants. In particular, we present polynomial algorithms for bounded degree trees and star of chains, as well as an approximation algorithm for bipartite graphs of maximum degree at most twelve which beats the best known approximation ratios.


Weighted edge coloring Polynomial algorithms Approximation algorithms 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Giorgio Lucarelli
    • 1
  • Ioannis Milis
    • 1
  • Vangelis T. Paschos
    • 2
  1. 1.Department of InformaticsAthens University of Economics and BusinessAthensGreece
  2. 2.LAMSADE, CNRS UMR 7024 and Université Paris-DauphineParisFrance

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