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An Erdős-Gallai Theorem for Matroids

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Abstract

Erdős and Gallai showed that for any simple graph with n vertices and circumference c it holds that \({{{\mid}{E(G)}{\mid} \leq {\frac{1}{2}}(n - 1)c}}\). We extend this theorem to simple binary matroids having no F 7-minor by showing that for such a matroid M with circumference c(M) ≥  3 it holds that \({{{\mid}{E(M)}{\mid} \leq {\frac{1}{2}}r(M)c(M)}}\).

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  1. Department of Mathematics, Thompson Rivers University, Kamloops, BC, V2C5N3, Canada

    Sean McGuinness

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  1. Sean McGuinness
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Correspondence to Sean McGuinness.

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McGuinness, S. An Erdős-Gallai Theorem for Matroids. Ann. Comb. 16, 107–119 (2012). https://doi.org/10.1007/s00026-011-0123-4

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  • DOI: https://doi.org/10.1007/s00026-011-0123-4

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