An algorithm for packing non-zero A-paths in group-labelled graphs


Let G = (V, E) be an oriented graph whose edges are labelled by the elements of a group Γ and let AV. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We give an efficient algorithm for finding a maximum collection of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem.

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Correspondence to Maria Chudnovsky.

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This research was partially conducted during the period Chudnovsky served as a Clay Mathematics Institute Long-Term Prize Fellow. The research was supported in part by the Natural Sciences and Engineering Council of Canada.

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Chudnovsky, M., Cunningham, W.H. & Geelen, J. An algorithm for packing non-zero A-paths in group-labelled graphs. Combinatorica 28, 145–161 (2008).

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Mathematics Subject Classification (2000)

  • 05C22