An attempt to classify bipartite graphs by their chromatic Polynomial.
For the purpose of tackling the four-colour problem, Birkhoff (1912) introduced the chromatic polynomial of a map, denoted by P(M,A), which is a number of proper Acolouring of a map M. Whitney (1932), who established many fundamental results for it, later generalized the notion of a chromatic polyno...
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| Format: | Monograph |
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Universiti Sains Malaysia
2009
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| _version_ | 1825832598988914688 |
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| author | Hasni, Roslan |
| author_facet | Hasni, Roslan |
| author_sort | Hasni, Roslan |
| collection | USM |
| description | For the purpose of tackling the four-colour problem, Birkhoff (1912) introduced the chromatic polynomial of a map, denoted by P(M,A), which is a number of proper Acolouring of a map M. Whitney (1932), who established many fundamental results for it, later generalized the notion of a chromatic polynomial to that of an arbitrary graph. In 1968, Read asked whether it is possible to find a set of necessary and sufficient algebraic conditions for a polynomial to be the chromatic polynomial of some graph. In particular, Read asked for a necessary and sufficient condition for two graphs to be chromatically equivalent; that is, to have the same chromatic polynomial. In 1978, Chao and Whitehead defined a graph to be chromatically unique if no other graphs share its chromatic
polynomial. Since then many researchers have been studying chromatic uniqueness and chromatic equivalence of graphs.
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| first_indexed | 2024-03-06T14:55:14Z |
| format | Monograph |
| id | usm.eprints-31793 |
| institution | Universiti Sains Malaysia |
| last_indexed | 2024-03-06T14:55:14Z |
| publishDate | 2009 |
| publisher | Universiti Sains Malaysia |
| record_format | dspace |
| spelling | usm.eprints-317932017-09-07T04:47:38Z http://eprints.usm.my/31793/ An attempt to classify bipartite graphs by their chromatic Polynomial. Hasni, Roslan QA Mathematics For the purpose of tackling the four-colour problem, Birkhoff (1912) introduced the chromatic polynomial of a map, denoted by P(M,A), which is a number of proper Acolouring of a map M. Whitney (1932), who established many fundamental results for it, later generalized the notion of a chromatic polynomial to that of an arbitrary graph. In 1968, Read asked whether it is possible to find a set of necessary and sufficient algebraic conditions for a polynomial to be the chromatic polynomial of some graph. In particular, Read asked for a necessary and sufficient condition for two graphs to be chromatically equivalent; that is, to have the same chromatic polynomial. In 1978, Chao and Whitehead defined a graph to be chromatically unique if no other graphs share its chromatic polynomial. Since then many researchers have been studying chromatic uniqueness and chromatic equivalence of graphs. Universiti Sains Malaysia 2009 Monograph NonPeerReviewed Hasni, Roslan (2009) An attempt to classify bipartite graphs by their chromatic Polynomial. Project Report. Universiti Sains Malaysia. (Submitted) |
| spellingShingle | QA Mathematics Hasni, Roslan An attempt to classify bipartite graphs by their chromatic Polynomial. |
| title | An attempt to classify bipartite graphs by their chromatic
Polynomial.
|
| title_full | An attempt to classify bipartite graphs by their chromatic
Polynomial.
|
| title_fullStr | An attempt to classify bipartite graphs by their chromatic
Polynomial.
|
| title_full_unstemmed | An attempt to classify bipartite graphs by their chromatic
Polynomial.
|
| title_short | An attempt to classify bipartite graphs by their chromatic
Polynomial.
|
| title_sort | attempt to classify bipartite graphs by their chromatic polynomial |
| topic | QA Mathematics |
| work_keys_str_mv | AT hasniroslan anattempttoclassifybipartitegraphsbytheirchromaticpolynomial AT hasniroslan attempttoclassifybipartitegraphsbytheirchromaticpolynomial |