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An Erdős–Gallai-Type Theorem for Keyrings

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Abstract

A keyring is a graph obtained by appending \(r \ge 1\) leaves to one of the vertices of a cycle. We prove that for every \(r \le (k-1)/2\), any graph with average degree more than \(k-1\) contains a keyring with r leaves and at least k edges.

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Acknowledgements

The author would like to thank the referees for their suggestions and comments.

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  1. Armonk, USA

    Alexander Sidorenko

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  1. Alexander Sidorenko
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Correspondence to Alexander Sidorenko.

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Sidorenko, A. An Erdős–Gallai-Type Theorem for Keyrings. Graphs and Combinatorics 34, 633–638 (2018). https://doi.org/10.1007/s00373-018-1901-0

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  • DOI: https://doi.org/10.1007/s00373-018-1901-0

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