On the complexity of generalized chromatic polynomials
Goodall, A. and Hermann, M. and Kotek, T. and Makowsky, J.A. and Noble, Steven (2017) On the complexity of generalized chromatic polynomials. Advances in Applied Mathematics 94 , pp. 71-102. ISSN 0196-8858.
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Abstract
J. Makowsky and B. Zilber (2004) showed that many variations of graph colorings, called CP-colorings in the sequel, give rise to graph polynomials. This is true in particular for harmonious colorings, convex colorings, mcctmcct-colorings, and rainbow colorings, and many more. N. Linial (1986) showed that the chromatic polynomial χ(G;X)χ(G;X) is #P#P-hard to evaluate for all but three values X=0,1,2X=0,1,2, where evaluation is in P. This dichotomy includes evaluation at real or complex values, and has the further property that the set of points for which evaluation is in P is finite. We investigate how the complexity of evaluating univariate graph polynomials that arise from CP-colorings varies for different evaluation points. We show that for some CP-colorings (harmonious, convex) the complexity of evaluation follows a similar pattern to the chromatic polynomial. However, in other cases (proper edge colorings, mcctmcct-colorings, H-free colorings) we could only obtain a dichotomy for evaluations at non-negative integer points. We also discuss some CP-colorings where we only have very partial results.
Metadata
| Item Type: | Article |
|---|---|
| Keyword(s) / Subject(s): | Graph polynomials, Counting complexity, Chromatic polynomial |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Administrator |
| Date Deposited: | 15 Jun 2017 09:04 |
| Last Modified: | 09 Aug 2023 12:41 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/18934 |
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