Document Type

Article

Publication Date

1-1-2023

Abstract

Jim Geelen and Peter Nelson proved that, for a loopless connected binary ma-troid M with an odd circuit, if a largest odd circuit of M has k elements, then a largest circuit of M has at most 2k − 2 elements. The goal of this note is to show that, when M is 3-connected, either M has a spanning circuit, or a largest circuit of M has at most 2k − 4 elements. Moreover, the latter holds when M is regular of rank at least four.

Publication Source (Journal or Book title)

Electronic Journal of Combinatorics

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