Improved approximation algorithms for the Max Edge-Coloring problem

The Max Edge-Coloring problem asks for a proper edge-coloring of an edge-weighted graph minimizing the sum of the weights of the heaviest edges in the color classes. In this paper we present a PTAS for trees and a 1.74-approximation algorithm for bipartite graphs; we also adapt the last algorithm to one for general graphs of the same, asymptotically, approximation ratio.

► We study the max edge-coloring problem of an edge-weighted graph.
► Minimize the sum of the weights of the heaviest edge in each color class.
► A PTAS for trees.
► A 1.74-approximation algorithm for bipartite graphs.
► An asymptotic 1.74-approximation algorithm for general graphs.