Complexity results for minimum sum edge coloring

Authors:
Dániel Marx
Affiliations:
Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest H-1521, Hungary
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

In the Minimum Sum Edge Coloring problem we have to assign positive integers to the edges of a graph such that adjacent edges receive different integers and the sum of the assigned numbers is minimal. We show that the problem is (a) NP-hard for planar bipartite graphs with maximum degree 3, (b) NP-hard for 3-regular planar graphs, (c) NP-hard for partial 2-trees, and (d) APX-hard for bipartite graphs.