b-matching degree-sequence polyhedra

Abstract

A capacitatedb-matching in a graph is an assignment of non-negative integers to edges, each at most a given capacity and the sum at each vertex at most a given bound. Its degree sequence is the vector whose components are the sums at each vertex. We give a linear-inequality description of the convex hull of degree sequences of capacitatedb-matchings of a graph. This result includes as special cases theorems of Balas-Pulleyblank on matchable sets and Koren on degree sequences of simple graphs. We also give a min-max separation theorem, and describe a connection with submodular functions.

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Part of this author's work was done at the Institut für Operations Research and the Forschungsinstitut für Diskrete Mathematik, Universität Bonn, Germany. Research supported by SFB303 DFG, Germany, and by NSERC of Canada.

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Cunningham, W.H., Green-Krótki, J. b-matching degree-sequence polyhedra. Combinatorica 11, 219–230 (1991). https://doi.org/10.1007/BF01205074

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AMS subject classification (1980)

  • 05 C 70
  • 15 A 39