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We address the problem of enumeration of seating arrangements of married couples around a circular table such that no spouses seat next to each other and no k consecutive persons are of the same gender. While the case of k = 2 corresponds to the classicalprobì eme des ménages with a well-studied solution, no closed-form expression for number of arrangements… (More)

A graph G = (V, E) is a pairwise compatibility graph (PCG) if there exists an edge-weighted tree T and two non-negative real numbers d min and d max such that each leaf u of T is a node of V and there is an edge (u, v) ∈ E if and only if d min ≤ d T (u, v) ≤ d max where d T (u, v) is the sum of weights of the edges on the unique path from u to v in T. The… (More)

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