Abstract A $(k, g) $-cage is a $ k $-regular graph of girth $ g $ of minimum order. In this
survey, we present the results of over 50 years of searches for cages. We present the …

In this paper, we study $ r $-uniform hypergraphs ${\cal H} $ without cycles of length less
than five, employing the definition of a hypergraph cycle due to Berge. In particular, for $ r …

We give a constructive and exhaustive definition of Kochen–Specker (KS) vectors in a
Hilbert space of any dimension as well as of all the remaining vectors of the space. KS …

Quantum contextuality supports quantum computation and communication. One of its main
vehicles is hypergraphs. The most elaborated are the Kochen–Specker ones, but there is …

Recently, quantum contextuality has been proved to be the source of quantum computation's
power. That, together with multiple recent contextual experiments, prompts improving the …

In quantum logical terms, Hardy-type arguments can be uniformly presented and extended
as collections of intertwined contexts and their observables. If interpreted classically, those …

We show that one can formulate an algebra with lattice ordering so as to contain one
quantum and five classical operations as opposed to the standard formulation of the Hilbert …

We introduce a contextual quantum system comprising mutually complementary
observables organized into two or more collections of pseudocontexts with the same …

Quantum contextuality turns out to be a necessary resource for universal quantum
computation and important in the field of quantum information processing. It is therefore of …

We show that all possible 388 4-dim Kochen–Specker (KS)(vector) sets (of yes–no
questions) with 18 through 23 vectors and 844 sets with 24 vectors all with component …