Chromatically unique bipartite graphs with certain 3-independent partition numbers III
For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0 , let ( ) 2 , K−s p q denote the set of 2_connected bipartite graphs which can be obtained from K(p,q) by deleting a set of s edges. In this paper, we prove that for any graph ( ) 2 G∈K−s p,q with p ≥ q ≥ 3 and 1 ≤ s ≤ q - 1 if the number of 3-independe...
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| Format: | Article |
| Language: | English |
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Universiti Putra Malaysia Press
2007
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| Online Access: | http://psasir.upm.edu.my/id/eprint/12564/ http://psasir.upm.edu.my/id/eprint/12564/1/page_139-162.pdf |
| _version_ | 1848841876040318976 |
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| author | Hasni @ Abdullah, Roslan Peng, Yee Hock |
| author_facet | Hasni @ Abdullah, Roslan Peng, Yee Hock |
| author_sort | Hasni @ Abdullah, Roslan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0 , let ( ) 2 , K−s p q denote the set of 2_connected bipartite graphs which can be obtained from K(p,q) by deleting a set
of s edges. In this paper, we prove that for any graph ( ) 2 G∈K−s p,q with p ≥ q ≥ 3 and 1 ≤ s ≤ q - 1 if the number of 3-independent partitions of G is 2p-1 + 2q-1 + s +
4, then G is chromatically unique. This result extends both a theorem by Dong et al.[2]; and results in [4] and [5]. |
| first_indexed | 2025-11-15T07:50:12Z |
| format | Article |
| id | upm-12564 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:50:12Z |
| publishDate | 2007 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-125642015-05-27T02:06:50Z http://psasir.upm.edu.my/id/eprint/12564/ Chromatically unique bipartite graphs with certain 3-independent partition numbers III Hasni @ Abdullah, Roslan Peng, Yee Hock For integers p, q, s with p ≥ q ≥ 2 and s ≥ 0 , let ( ) 2 , K−s p q denote the set of 2_connected bipartite graphs which can be obtained from K(p,q) by deleting a set of s edges. In this paper, we prove that for any graph ( ) 2 G∈K−s p,q with p ≥ q ≥ 3 and 1 ≤ s ≤ q - 1 if the number of 3-independent partitions of G is 2p-1 + 2q-1 + s + 4, then G is chromatically unique. This result extends both a theorem by Dong et al.[2]; and results in [4] and [5]. Universiti Putra Malaysia Press 2007 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12564/1/page_139-162.pdf Hasni @ Abdullah, Roslan and Peng, Yee Hock (2007) Chromatically unique bipartite graphs with certain 3-independent partition numbers III. Malaysian Journal of Mathematical Sciences, 1 (1). pp. 139-162. ISSN 1823-8343 http://einspem.upm.edu.my/journal/volume1.1.php |
| spellingShingle | Hasni @ Abdullah, Roslan Peng, Yee Hock Chromatically unique bipartite graphs with certain 3-independent partition numbers III |
| title | Chromatically unique bipartite graphs with certain 3-independent partition numbers III |
| title_full | Chromatically unique bipartite graphs with certain 3-independent partition numbers III |
| title_fullStr | Chromatically unique bipartite graphs with certain 3-independent partition numbers III |
| title_full_unstemmed | Chromatically unique bipartite graphs with certain 3-independent partition numbers III |
| title_short | Chromatically unique bipartite graphs with certain 3-independent partition numbers III |
| title_sort | chromatically unique bipartite graphs with certain 3-independent partition numbers iii |
| url | http://psasir.upm.edu.my/id/eprint/12564/ http://psasir.upm.edu.my/id/eprint/12564/ http://psasir.upm.edu.my/id/eprint/12564/1/page_139-162.pdf |