Conjecture on Hamilton Cycles in Digraphs of Unitary Matrices
نویسندگان
چکیده
We conjecture new sufficient conditions for a digraph to have a Hamilton cycle. In view of applications, the conjecture is of interest in the areas where unitary matrices are of importance including quantum mechanics and quantum computing.
منابع مشابه
Hamilton cycles in digraphs of unitary matrices
A set S ⊆ V is called an q-set (q−-set, respectively) if S has at least two vertices and, for every u ∈ S, there exists v ∈ S, v 6= u such that N(u) ∩ N(v) 6= ∅ (N−(u)∩N−(v) 6= ∅, respectively). A digraph D is called s-quadrangular if, for every q-set S, we have | ∪ {N+(u) ∩ N(v) : u 6= v, u, v ∈ S}| ≥ |S| and, for every q−set S, we have | ∪ {N−(u) ∩ N−(v) : u, v ∈ S)} ≥ |S|. We conjecture that...
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