On 2-partitionable clutters and the MFMC property

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dc.creatorFlores-Méndez, Alejandro
dc.creatorGitler, Isidoro
dc.creatorReyes, Enrique
dc.date2008-06-11
dc.date.accessioned2026-07-07T09:43:41Z
dc.date.available2026-07-07T09:43:41Z
dc.descriptionWe introduce 2-partitionable clutters as the simplest case of the class of $k$-partitionable clutters and study some of their combinatorial properties. In particular, we study properties of the rank of the incidence matrix of these clutters and properties of their minors. A well known conjecture of Conforti and Cornuéjols \cite{ConfortiCornuejols,cornu-book} states: That all the clutters with the packing property have the max-flow min-cut property, i.e. are mengerian. Among the general classes of clutters known to verify the conjecture are: balanced clutters (Fulkerson, Hoffman and Oppenheim \cite{FulkersonHoffmanOppenheim}), binary clutters (Seymour \cite{Seymour}) and dyadic clutters (Cornuéjols, Guenin and Margot \cite{CornuejolsGueninMargot}). We find a new infinite family of 2-partitionable clutters, that verifies the conjecture. On the other hand we are interested in studying the normality of the Rees algebra associated to a clutter and possible relations with the Conforti and Cornuéjols conjecture. In fact this conjecture is equivalent to an algebraic statement about the normality of the Rees algebra \cite{rocky}.
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0806.1772
dc.identifierhttp://arxiv.org/abs/0806.1772
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162653
dc.subjectCommutative Algebra
dc.titleOn 2-partitionable clutters and the MFMC property
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