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

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 classical problème des ménages with a well-studied solution, no closed-form expression for number of arrangements… (More)

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