Affiliation:
1. Aix Marseille Université/CNRS
Abstract
The notion of graph acyclicity has been extended to several notions of hypergraph acyclicity. In increasing order of generality:
gamma
acyclicity,
beta
acyclicity, and
alpha
acyclicity have met a great interest in many fields.
For each notion, we prove the equivalence between the numerous characterizations with a new, simpler proof, in a self-contained manner. For that purpose, we introduce new notions of alpha, beta, and gamma leaf that allow one to define new “rule-based” characterizations of each notion.
The combined presentation of the notions is completed with a study of their respective closure properties. New closure results are established, and alpha, beta, and gamma acyclicity are proved optimal w.r.t. their closure properties.
Funder
French Agence Nationale de la Recherche, ARCHIMEDE LabEx
A*MIDEX project
Publisher
Association for Computing Machinery (ACM)
Subject
General Computer Science,Theoretical Computer Science
Cited by
23 articles.
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