International audience

Abstract Given a 3-uniform hypergraph H having a set V of vertices, and a set of hyperedges $$T\subset \mathcal {P}(V)$$ T ⊂ P ( V ) , whose elements have cardinality three each, a null labelling is an assignment of $$\pm 1$$ ± 1 to the hyperedges such that each vertex belongs to the same number of hyperedges labelled $$+1$$ + 1 and $$-1$$ - 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.

It is commonly accepted that the various parts of the human brain interact as a network at macroscopic, mesoscopic and microscopic level. Recently, different network models have been proposed to mime the brain behavior both at resting state and during tasks: Our study concerns one of those model th at consider both the physical and functional connectivity as well as topological metrics of the brain networks. We provide evidence of the soundness of the model by means of a synthetic dataset based on the existing literature concerning the active cerebral areas at the resting state. Furthermore, we consider Ruzicka similarity measure in order to stress the predictive capability of the model and provide a thresholding criterium. Some network statistics are finally provided.

In this paper we give a combinatorial interpretation of linear recurrences having constant coefficients. In particular, we describe a recursive construction for a language ℒ such that the words in ℒ having length n satisfy the given recurrence and avoid a cross-bifix-free set of patterns.

In this paper we study the enumeration and the construction of particular binary words avoiding the pattern 1j+1 0j . By means of the theory of Riordan arrays, we solve the enumeration problem and we give a particular succession rule, called jumping

Cross-bifix-free sets are sets of words such that no prefix of any word is a suffix of any other word. In this paper, we introduce a general constructive method for the sets of cross-bifix-free binary words of fixed length. It enables us to determine a cross-bifix-free words subset which has the property to be non-expandable.