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Optimal cocircuits in regular matroids and applications

✍ Scribed by Horst Hamacher

Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
554 KB
Volume
8
Category
Article
ISSN
0377-0427

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We consider the cocircuit graph G M of an oriented matroid M, which is the 1-skeleton of the cell complex formed by the span of the cocircuits of M. As a result of Cordovil, Fukuda, and Guedes de Oliveira, the isomorphism class of M is not determined by G M , but it is determined if M is uniform and

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## Abstract Jensen and Toft 8 conjectured that every 2‐edge‐connected graph without a __K__~5~‐minor has a nowhere zero 4‐flow. Walton and Welsh 19 proved that if a coloopless regular matroid __M__ does not have a minor in {__M__(__K__~3,3~), M\*(__K__~5~)}, then __M__ admits a nowhere zero 4‐flow.