Transitive oriented 3-Hypergraphs of cyclic orders
Natalia Garcia-Colin, Amanda Montejano, Luis Montejano, Deborah, Oliveros
TL;DR
This paper introduces a new concept of transitivity for oriented 3-hypergraphs to analyze cyclic orders, providing conditions for extension and characterizations related to cyclic permutations.
Contribution
It defines transitivity for oriented 3-hypergraphs and characterizes cyclic orders and their extensions using this new framework.
Findings
Provided sufficient conditions for partial cyclic orders to be extendable
Characterized 3-hypergraphs associated with cyclic permutations
Connected cyclic orders with hypergraph properties
Abstract
In this paper we introduce the definition of transitivity for oriented 3-hypergraphs in order to study partial and complete cyclic orders. This definition allow us to give sufficient conditions on a partial cyclic order to be totally extendable. Furthermore, we introduce the 3-hypergraph associated to a cyclic permutation and characterize it in terms of cyclic comparability 3-hypergraphs.
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Taxonomy
Topicsgraph theory and CDMA systems · Finite Group Theory Research · Limits and Structures in Graph Theory