The parity problem of polymatroids without double circuits

Abstract

According to the present state of the theory of the matroid parity problem, the existence of a good characterization to the size of a maximum matching depends on the behavior of certain substructures, called double circuits. In this paper we prove that if a polymatroid has no double circuits then a partition type min-max formula characterizes the size of a maximum matching. Applications to parity constrained orientations and to a rigidity problem are given.

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Correspondence to Jácint Szabó.

Additional information

Research is supported by OTKA grants K60802, TS049788 and by European MCRTN Adonet, Contract Grant No. 504438.

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Makai, M., Szabó, J. The parity problem of polymatroids without double circuits. Combinatorica 28, 679–692 (2008). https://doi.org/10.1007/s00493-008-2374-1

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Mathematics Subject Classification (2000)

  • 05B35