Chromatic polynomials
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 po...
| Main Author: | |
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| Format: | Thesis (University of Nottingham only) |
| Language: | English |
| Published: |
1994
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| Online Access: | https://eprints.nottingham.ac.uk/13978/ |
| _version_ | 1848791852017254400 |
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| author | Wakelin, Christopher David |
| author_facet | Wakelin, Christopher David |
| author_sort | Wakelin, Christopher David |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T18:35:05Z |
| format | Thesis (University of Nottingham only) |
| id | nottingham-13978 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T18:35:05Z |
| publishDate | 1994 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-139782025-02-28T11:28:12Z https://eprints.nottingham.ac.uk/13978/ Chromatic polynomials Wakelin, Christopher David 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. 1994 Thesis (University of Nottingham only) NonPeerReviewed application/pdf en arr https://eprints.nottingham.ac.uk/13978/1/259639.pdf Wakelin, Christopher David (1994) Chromatic polynomials. PhD thesis, University of Nottingham. |
| spellingShingle | Wakelin, Christopher David Chromatic polynomials |
| title | Chromatic polynomials |
| title_full | Chromatic polynomials |
| title_fullStr | Chromatic polynomials |
| title_full_unstemmed | Chromatic polynomials |
| title_short | Chromatic polynomials |
| title_sort | chromatic polynomials |
| url | https://eprints.nottingham.ac.uk/13978/ |