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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Main Authors: Hasni @ Abdullah, Roslan, Peng, Yee Hock
Format: Article
Language:English
Published: Universiti Putra Malaysia Press 2007
Online Access:http://psasir.upm.edu.my/id/eprint/12564/
http://psasir.upm.edu.my/id/eprint/12564/1/page_139-162.pdf
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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].
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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