List edge multicoloring in graphs with few cycles

Authors:
Dániel Marx
Affiliations:
Department of Computer Science and Information Theory, Budapest University of Technology and Economics, H-1521 Budapest, Hungary
Venue:
Information Processing Letters
Year:
2004

Citing 3
Cited 0

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Combinatorica
Extending an edge-coloring

Journal of Graph Theory
The Complexity of Tree Multicolorings

MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science

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Abstract

The list edge multicoloring problem is a version of edge coloring where every edge e has a list of available colors L(e) and an integer demand x(e). For each e, we have to select x(e) colors from L(e) such that adjacent edges receive disjoint sets of colors. Marcotte and Seymour proved a characterization theorem for list edge multicoloring trees, which can be turned into a polynomial time algorithm. We present a slightly more general algorithm that works also on odd cycles. A variant of the method leads to a randomized polynomial time algorithm for handling even cycles as well.