Graphical Eulerian numbers and chromatic generating functions

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In this paper some further properties of the coefficients of a chromatic generating function introduced by Linial are proved. A combinatorial interpretation of these numbers is given by specializing some results of Stanley on posets to surjective n-colorings of a graph G of order n compatible with linear orders on V(G) which extend acyclic orientations of G. If G is composed from n isolated vertices these coefficients are classical Eulerian numbers A(n, k). © 1987.




Tomescu, I. (1987). Graphical Eulerian numbers and chromatic generating functions. Discrete Mathematics, 66(3), 315–318.

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