On Laminar Matroids and b-Matchings
نویسندگان
چکیده
We prove that three matroid optimisation problems, namely, the matchoid, matroid parity and matroid matching problems, all reduce to the b-matching problem when the matroids concerned are laminar. We then use this equivalence to show that laminar matroid parity polytopes are affinely congruent to b-matching polytopes, and have Chvátal rank equal to one. On the other hand, we prove that laminar matroid parity polytopes can have facet-defining inequalities that have left-hand side coefficients greater than 2.
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