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Article Dans Une Revue Algorithmica Année : 2023

Structure and Complexity of 2-Intersection Graphs of 3-Hypergraphs

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Abstract Given a 3-uniform hypergraph H having a set V of vertices, and a set of hyperedges $T\subset \mathcal {P}(V)$, whose elements have cardinality three each, a null labelling is an assignment of $\pm 1$ to the hyperedges such that each vertex belongs to the same number of hyperedges labelled +1 and -1. A sufficient condition for the existence of a null labelling of H (proved in Di Marco et al. Lect Notes Comput Sci 12757:282–294, 2021) is a Hamiltonian cycle in its 2-intersection graph. The notion of 2-intersection graph generalizes that of intersection graph of an (hyper)graph and extends its effectiveness. The present study first shows that this sufficient condition for the existence of a null labelling in H can not be weakened by requiring only the connectedness of the 2-intersection graph. Then some interesting properties related to their clique configurations are proved. Finally, the main result is proved, the NP-completeness of this characterization and, as a consequence, of the construction of the related 3-hypergraphs.

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hal-03708146 , version 1 (29-06-2022)

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Niccoló Di Marco, Andrea Frosini, William Lawrence Kocay, Elisa Pergola, Lama Tarsissi. Structure and Complexity of 2-Intersection Graphs of 3-Hypergraphs. Algorithmica, 2023, 85, pp.745-761. ⟨10.1007/s00453-022-00990-4⟩. ⟨hal-03708146⟩
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