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We discuss chromatic constructions on orthogonality hypergraphs which are classical set representable or have a faithful orthogonal representation. The latter ones have a quantum mechanical realization in terms of intertwined contexts or maximal observables. Structure reconstruction of these hypergraphs from their table of two-valued states is possible for a class of hypergraphs, namely perfectly separable hypergraphs. Some examples from exempt categories that either cannot be reconstructed by two-valued states or whose set of two-valued states does not yield a coloring are presented.
Contextuality is a fundamental feature of quantum theory and is necessary for quantum computation and communication. Serious steps have therefore been taken towards a formal framework for contextuality as an operational resource. However, the most im
Quantum measurements are noncontextual, with outcomes independent of which other commuting observables are measured at the same time, when consistently analyzed using principles of Hilbert space quantum mechanics rather than classical hidden variables.
We study in this paper the structure of solutions in the random hypergraph coloring problem and the phase transitions they undergo when the density of constraints is varied. Hypergraph coloring is a constraint satisfaction problem where each constrai
Motivated by the ErdH{o}s-Faber-Lov{a}sz (EFL) conjecture for hypergraphs, we consider the list edge coloring of linear hypergraphs. We show that if the hyper-edge sizes are bounded between $i$ and $C_{i,epsilon} sqrt{n}$ inclusive, then there is a l