Matricial characterization of tournaments with maximum number of diamonds

被引：4

作者：

Belkouche, Wiam ^{[1
]}

Boussairi, Abderrahim ^{[1
]}

Lakhlifi, Soufiane ^{[1
]}

Zaidi, Mohamed ^{[1
]}

机构：

[1] Univ Hassan 2, Fac Sci Ain Chock, Dept Math & Informat, Lab Topol Algebre Geometr & Math Discretes, Km 8 Route El Jadida,BP 5366 Maarif, Casablanca, Morocco

来源：

DISCRETE MATHEMATICS | 2020年 / 343卷 / 04期

关键词：

Tournaments; Diamonds; Skew-conference matrices; EW-matrices; Spectrum;

D O I：

10.1016/j.disc.2019.111699

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A diamond is a 4-tournament which consists of a vertex dominating or dominated by a 3-cycle. Assuming the existence of skew-conference matrices, we give a complete characterization of n-tournaments with the maximum number of diamonds when n equivalent to 0 (mod 4) and n equivalent to 3 (mod 4). For n equivalent to 2 (mod 4), we obtain an upper bound on the number of diamonds in an n-tournament and we give a matricial characterization of tournaments achieving this bound. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：9

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