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Extremal \(K_4\)-minor-free graphs without short cycles

We determine the maximum number of edges in a \(K_4\)-minor-free \(n\)-vertex graph of girth \(g\), when \(g = 5\) or \(g\) is even. We argue that there are many different \(n\)-vertex extremal graphs, if \(n\) is even and \(g\) is odd.

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Bibliographic Details
Published in:arXiv.org 2021-11
Main Author: Barát, János
Format: Article
Language:English
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Summary:We determine the maximum number of edges in a \(K_4\)-minor-free \(n\)-vertex graph of girth \(g\), when \(g = 5\) or \(g\) is even. We argue that there are many different \(n\)-vertex extremal graphs, if \(n\) is even and \(g\) is odd.
ISSN:2331-8422