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Combinatorica

, Volume 38, Issue 4, pp 861–885 | Cite as

How Many Circuits Determine an Oriented Matroid?

  • Kolja KnauerEmail author
  • Luis Pedro Montejano
  • Jorge Luis Ramírez Alfonsín
Article
  • 69 Downloads

Abstract

Las Vergnas and Hamidoune studied the number of circuits needed to determine an oriented matroid. In this paper we investigate this problem and some new variants, as well as their interpretation in particular classes of matroids. We present general upper and lower bounds in the setting of general connected orientable matroids, leading to the study of subgraphs of the base graph and the intersection graph of circuits.

We then consider the problem for uniform matroids which is closely related to the notion of (connected) covering numbers in Design Theory. Finally, we also devote special attention to regular matroids as well as some graphic and cographic matroids leading in particular to the topics of (connected) bond and cycle covers in Graph Theory.

Mathematics Subject Classification (2000)

52C40 05B35 

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Copyright information

© János Bolyai Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Kolja Knauer
    • 1
    • 2
    Email author
  • Luis Pedro Montejano
    • 3
  • Jorge Luis Ramírez Alfonsín
    • 3
  1. 1.Laboratoire d’Informatique FondamentaleAix-Marseille UniversitéMarseille Cedex 09France
  2. 2.CNRS Faculté des Sciences de LuminyMarseille Cedex 09France
  3. 3.Université de Montpellier Institut Montpelliérain Alexander Grothendieck Case Courrier 051 Place Eugène BataillonMontpellier Cedex 05France

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