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Article Dans Une Revue Discrete Applied Mathematics Année : 2021

On Null 3-Hypergraphs

Andrea Frosini
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William L Kocay
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Giulia Palma
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Résumé

Given a 3-uniform hypergraph H consisting of a set V of vertices, and T ⊆ V 3 triples, a null labelling is an assignment of ±1 to the triples such that each vertex is contained in an equal number of triples labelled +1 and −1. Thus, the signed degree of each vertex is zero. A necessary condition for a null labelling is that the degree of every vertex of H is even. The Null Labelling Problem is to determine whether H has a null labelling. It is proved that this problem is NP-complete. Computer enumerations suggest that most hypergraphs which satisfy the necessary condition do have a null labelling. Some constructions are given which produce hypergraphs satisfying the necessary condition, but which do not have a null labelling. A self complementary 3-hypergraph with this property is also constructed.
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Dates et versions

hal-03058519 , version 1 (11-12-2020)

Identifiants

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Andrea Frosini, William L Kocay, Giulia Palma, Lama Tarsissi. On Null 3-Hypergraphs. Discrete Applied Mathematics, 2021, 303, pp.76-85. ⟨10.1016/j.dam.2020.10.020⟩. ⟨hal-03058519⟩
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