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...
Saved in:
| Main Authors: | , |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Universiti Putra Malaysia |
| Language: | English |
| Summary: | 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]. |
|---|