Extensions and presentations of transversal matroids

نویسندگان

  • Joseph E. Bonin
  • Anna de Mier
چکیده

A transversal matroid M can be represented by a collection of sets, called a presentation of M , whose partial transversals are the independent sets of M . Minimal presentations are those for which removing any element from any set gives a presentation of a different matroid. We study the connections between (single-element) transversal extensions of M and extensions of presentations of M . We show that a presentation of M is minimal if and only if different extensions of it give different extensions of M ; also, all transversal extensions ofM can be obtained by extending the minimal presentations of M . We also begin to explore the partial order that the weak order gives on the transversal extensions ofM . In Memory of Michel Las Vergnas

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عنوان ژورنال:
  • Eur. J. Comb.

دوره 50  شماره 

صفحات  -

تاریخ انتشار 2015