Advances and Applications in Discrete Mathematics
Volume 2, Issue 1, Pages 59 - 84
(July 2008)
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ON 2-PARTITIONABLE CLUTTERS AND THE MFMC PROPERTY
Alejandro Flores-Méndez (México), Isidoro Gitler (México) and Enrique Reyes (México)
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Abstract: We 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.
We give a new characterization of mengerian clutters, and we use it to find
a new infinite family of 2-partitionable clutters, that verifies the conjecture
of Conforti and Cornuéjols [1, 2].
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 [6]. |
Keywords and phrases: max-flow min-cut, mengerian, clutters, hypergraphs, normality, Rees algebras. |
Submitted by Shalom Eliahou |
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