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The minimum perfect matching in pseudo-dimension 0 < q < 1

Part of: Graph theory Combinatorial probability

Published online by Cambridge University Press:  27 October 2020

Joel Larsson
Joel Larsson*
Affiliation:
Department of Statistics, Lund University, Lund, Scania, Sweden
*
Email: [email protected]
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Abstract

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It is known that for Kn,n equipped with i.i.d. exp (1) edge costs, the minimum total cost of a perfect matching converges to $\zeta(2)=\pi^2/6$ in probability. Similar convergence has been established for all edge cost distributions of pseudo-dimension $q \geq 1$ . In this paper we extend those results to all real positive q, confirming the Mézard–Parisi conjecture in the last remaining applicable case.

MSC classification

Primary: 05C80: Random graphs
Secondary: 60C05: Combinatorial probability
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 30 , Issue 3 , May 2021 , pp. 374 - 397
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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