Chromatically unique bipartite graphs with certain 3-independent partition numbers III

• 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/12564/1/page_139-162.pdf; http://psasir.upm.edu.my/id/eprint/12564/; http://einspem.upm.edu.my/journal/volume1.1.php
• Institution: Universiti Putra Malaysia

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].