Informace o publikaci

CYCLES OF LENGTH THREE AND FOUR IN TOURNAMENTS

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CHAN Timothy Fong Nam GRZESIK Andrzej KRÁĽ Daniel NOEL Jonathan Andrew

Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj Acta Mathematica Universitatis Comenianae
Fakulta / Pracoviště MU

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Citace
www http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1222
Klíčová slova Tournaments; extremal combinatorics
Popis Linial and Morgenstern conjectured that, among all n-vertex tournaments with d((n)(3)) cycles of length three, the number of cycles of length four is asymptotically minimized by a random blow-up of a transitive tournament with all but one part of equal size and one smaller part. We prove the conjecture for d >= 1/36 by analyzing the possible spectrum of adjacency matrices of tournaments. We also demonstrate that the family of extremal examples is broader than expected and give its full description for d >= 1/16.