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Graphical Eulerian numbers and chromatic generating functions

✍ Scribed by Ioan Tomescu


Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
217 KB
Volume
66
Category
Article
ISSN
0012-365X

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✦ Synopsis


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.


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## Abstract Let __f__(__n__) = min{Ο‡(__G__ × __H__) : __G__ and __H__ are __n__‐chromatic digraphs} and __g__(__n__) = min{Ο‡(__G__ × __H__) : __G__ and __H__ are __n__‐chromatic graphs}. We prove that __f__ is bounded if and only if __g__ is bounded. Β© 2005 Wiley Periodicals, Inc. J Graph Theory