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Title: Some problems on chromatic polynomials

Abstract: A proper \lambda-coloring of a graph G is an assignment of colors to the vertices of G, with the property that adjacent vertices are assigned different colors. It is well known that the number of proper \lambda-colorings is given by a polynomial, P(G;\lambda), known as the chromatic polynomial of G. The object of this presentation is to describe several unsolved problems on chromatic polynomials with a brief account of their progress. Emphasis is given to problems related to findining sharp upper and lower bounds for chromatic polynomials.

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