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3-uniform hypergraphs: modular decomposition and realization by tournaments

Abstract

Let $H$ be a 3-uniform hypergraph. A tournament $T$ defined on $V(T)=V(H)$ is a realization of $H$ if the edges of $H$ are exactly the 3-element subsets of $V(T)$ that induce 3-cycles. We characterize the 3-uniform hypergraphs that admit realizations by using a suitable modular decomposition.

Dates and versions

hal-02014311 , version 1 (11-02-2019)

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Abderrahim Boussaïri, Brahim Chergui, Pierre Ille, Mohamed Zaïdi. 3-uniform hypergraphs: modular decomposition and realization by tournaments. 2018. ⟨hal-02014311⟩
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