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 443
The realization of k-uniform hypergraphs by tournaments
Soufiane Lakhlifi, Wiam Belkouche, Abderrahim Boussaïri
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 31, 2022
March 03, 2372
April 15, 2372

Abstract: We say that an 3-uniform hypergraph H = (V, H) is realizable if there exists an tournament with the same vertex set V for which the set of 3 cycles is exactly the hyperedges of H. Boussaïri et al. (2003) considered the problem of the characterization of 3-uniform hypergraphs. For 4-uniform hypergraphs, we consider the realization by taking the diamonds of tournaments. Recall that a diamond is the 4-tournament with a unique 3-cycle. We show that the problem of determining whether a 4-uniform hypergraph is realizable, can be reduced to one for 3-uniform hypergraphs. Moreover, we prove that ...