Abstract
A 3-uniform hypergraph H consists of a set V of vertices, and \(E\subseteq {V\atopwithdelims ()3}\) triples. Let a null labelling be an assignment of \(\pm 1\) to the triples such that each vertex has signed degree equal to zero. Assumed as necessary condition the degree of every vertex of H to be even, the Null Labelling Problem consists in determining whether H has a null labelling. Although the problem is NP-complete, the subclasses where the problem turns out to be polynomially solvable are of interest. In this study we define the notion of 2-intersection graph related to a 3-uniform hypergraph, and we prove that the existence of a Hamiltonian cycle there, is sufficient to obtain a null labelling in the related hypergraph. The proof we propose provides an efficient way of computing the null labelling.
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Di Marco, N., Frosini, A., Kocay, W.L. (2021). A Study on the Existence of Null Labelling for 3-Hypergraphs. In: Flocchini, P., Moura, L. (eds) Combinatorial Algorithms. IWOCA 2021. Lecture Notes in Computer Science(), vol 12757. Springer, Cham. https://doi.org/10.1007/978-3-030-79987-8_20
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DOI: https://doi.org/10.1007/978-3-030-79987-8_20
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