Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 535
Tournaments with maximum number of diamonds
Zaidi Mohamed, Belkouche Wiam, Boussairi Abderrahim, Lakhlifi Soufiane
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
February 19, 2022
March 03, 2436
April 15, 2436

Abstract: A diamond is a 4-tournament which consists of a vertex dominating or dominated by a 3-cycle. Assuming the existence of skewconference matrices, we give a complete characterization of n-tournaments with the maximum number of diamonds when n ≡ 0 (mod 4) and n ≡ 3 (mod 4). For n ≡ 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.