# A new two-variable generalization of the chromatic polynomial

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No abstract available.

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Let P(G; x; y) be the number of vertex colorings &phi : V â†’ {1,...,x} of an undirected graph G = (V, E) such that for all edges { u, v} â‰ E the relations &phi(v) â‰¤ y and Ï†(v) â‰¤ y implyÏ†(u) â‰ Ï†(v). We show that P(G; x, y) is a polynomial in x and y which...

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In this paper, we provide properties-which are, to the best of our knowledge, new-of the zeros of the polynomials belonging to the Askey scheme. These findings include Diophantine relations satisfied by these zeros when the parameters characterizing these polynomials are appropriately restricted.