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Explicit 𝑁-vertex graphs with maximum degree 𝐾 and diameter [1+π‘œ(1)]log𝐾-1 𝑁 for each 𝐾-1 a prime power

Published: 23 June 2019 Publication History

Abstract

Here we first present the solution of a long-standing open question–the explicit construction of an infinite family of N-vertex cubic graphs that have diameter [1+o(1)]log2 N. We then extend the techniques to construct, for each K of the form 2s+1 or K=ps+1; s an integer and p a prime, an infinite family of K-regular graphs on N vertices with diameter [1+o(1)]logKβˆ’1 N.

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Index Terms

  1. Explicit 𝑁-vertex graphs with maximum degree 𝐾 and diameter [1+π‘œ(1)]log𝐾-1 𝑁 for each 𝐾-1 a prime power

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    cover image ACM Conferences
    STOC 2019: Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing
    June 2019
    1258 pages
    ISBN:9781450367059
    DOI:10.1145/3313276
    Β© 2019 Association for Computing Machinery. ACM acknowledges that this contribution was authored or co-authored by an employee, contractor or affiliate of the United States government. As such, the United States Government retains a nonexclusive, royalty-free right to publish or reproduce this article, or to allow others to do so, for Government purposes only.

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    Published: 23 June 2019

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    Author Tags

    1. Explicit Constructions
    2. Extremal Graph Theory

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