Chromatically Unique Bipartite Graphs With Certain 3-independent Partition Numbers III
Roslan, Hasni 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
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.; and results in  and .
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