Chromatic polynomials

Wakelin, Christopher David (1994) Chromatic polynomials. PhD thesis, University of Nottingham.

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Abstract

In this thesis, we shall investigate chromatic polynomials of graphs, and some related polynomials. In Chapter 1, we study the chromatic polynomial written in a modified form, and use these results to characterise the chromatic polynomials of polygon trees. In Chapter 2, we consider the chromatic polynomial written as a sum of the chromatic polynomials of complete graphs; in particular, we determine for which graphs the coefficients are symmetrical, and show that the coefficients exhibit a skewed property. In Chapter 3, we dualise many results about chromatic polynomials to flow polynomials, including the results in Chapter 1, and a result about a zero-free interval. Finally, in Chapter 4, we investigate the zeros of the Tutte Polynomial; in particular their observed proximity to certain hyperbole in the xy-plane.

Item Type: Thesis (University of Nottingham only) (PhD)
Supervisors: Woodall, D.R.
Subjects: Q Science > QA Mathematics > QA150 Algebra
Faculties/Schools: UK Campuses > Faculty of Science > School of Mathematical Sciences
Item ID: 13978
Depositing User: EP, Services
Date Deposited: 10 Feb 2014 12:11
Last Modified: 14 Sep 2016 10:05
URI: http://eprints.nottingham.ac.uk/id/eprint/13978

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