Chromatic equivalence classes of some families of complete tripartite graphs
We obtain new necessary conditions on a graph which shares the same chromatic polynomial as that of the complete tripartite graph Km,n,r. Using these, we establish the chromatic equivalence classes for K1,n,n+1 (where n ≥ 2). This gives a partial solution to a question raised earlier by the authors....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Malaysian Mathematical Sciences Society
2014
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| Subjects: | |
| Online Access: | http://eprints.sunway.edu.my/273/ http://eprints.sunway.edu.my/273/1/Chromatic%20equivalence_HoCK%20%282%29.pdf |
| _version_ | 1848801789063725056 |
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| author | Chia, G. L. Ho, Chee-Kit * |
| author_facet | Chia, G. L. Ho, Chee-Kit * |
| author_sort | Chia, G. L. |
| building | SU Institutional Repository |
| collection | Online Access |
| description | We obtain new necessary conditions on a graph which shares the same chromatic polynomial as that of the complete tripartite graph Km,n,r. Using these, we establish the chromatic equivalence classes for K1,n,n+1 (where n ≥ 2). This gives a partial solution to a question raised earlier by the authors. With the same technique, we further show that Kn−3,n,n+1 is chromatically unique if n ≥ 5. In the more general situation, we show that if 2 ≤ m ≤ n, then Km,n,n+1 is chromatically unique if n is sufficiently large.
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| first_indexed | 2025-11-14T21:13:02Z |
| format | Article |
| id | sunway-273 |
| institution | Sunway University |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T21:13:02Z |
| publishDate | 2014 |
| publisher | Malaysian Mathematical Sciences Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | sunway-2732019-07-04T08:05:53Z http://eprints.sunway.edu.my/273/ Chromatic equivalence classes of some families of complete tripartite graphs Chia, G. L. Ho, Chee-Kit * QA Mathematics We obtain new necessary conditions on a graph which shares the same chromatic polynomial as that of the complete tripartite graph Km,n,r. Using these, we establish the chromatic equivalence classes for K1,n,n+1 (where n ≥ 2). This gives a partial solution to a question raised earlier by the authors. With the same technique, we further show that Kn−3,n,n+1 is chromatically unique if n ≥ 5. In the more general situation, we show that if 2 ≤ m ≤ n, then Km,n,n+1 is chromatically unique if n is sufficiently large. Malaysian Mathematical Sciences Society 2014 Article PeerReviewed text en http://eprints.sunway.edu.my/273/1/Chromatic%20equivalence_HoCK%20%282%29.pdf Chia, G. L. and Ho, Chee-Kit * (2014) Chromatic equivalence classes of some families of complete tripartite graphs. Bulletin of the Malaysian Mathematical Sciences Society, 37 (3). pp. 641-646. http://www.emis.de/journals/BMMSS/pdf/v37n3/v37n3p3.pdf |
| spellingShingle | QA Mathematics Chia, G. L. Ho, Chee-Kit * Chromatic equivalence classes of some families of complete tripartite graphs |
| title | Chromatic equivalence classes of some families of complete
tripartite graphs |
| title_full | Chromatic equivalence classes of some families of complete
tripartite graphs |
| title_fullStr | Chromatic equivalence classes of some families of complete
tripartite graphs |
| title_full_unstemmed | Chromatic equivalence classes of some families of complete
tripartite graphs |
| title_short | Chromatic equivalence classes of some families of complete
tripartite graphs |
| title_sort | chromatic equivalence classes of some families of complete
tripartite graphs |
| topic | QA Mathematics |
| url | http://eprints.sunway.edu.my/273/ http://eprints.sunway.edu.my/273/ http://eprints.sunway.edu.my/273/1/Chromatic%20equivalence_HoCK%20%282%29.pdf |