Skip to Main content Skip to Navigation
Journal articles

How Many Circuits Determine an Oriented Matroid?

Abstract : Las Vergnas & 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [36 references]  Display  Hide  Download
Contributor : Cathy Araspin <>
Submitted on : Monday, February 25, 2019 - 3:16:18 PM
Last modification on : Monday, May 11, 2020 - 11:00:11 AM
Long-term archiving on: : Sunday, May 26, 2019 - 3:19:20 PM


Files produced by the author(s)



Kolja Knauer, Luis Montejano, Jorge Luis Ramírez Alfonsín. How Many Circuits Determine an Oriented Matroid?. Combinatorica, Springer Verlag, 2018, 38 (4), pp.861-885. ⟨10.1007/s00493-016-3556-x⟩. ⟨hal-02048407⟩



Record views


Files downloads