Volume 28 • Number 2 • 2006   • Chromatically Unique Bipartite Graphs with Certain 3-independent Partition Numbers II Roslan Hasni and Y.H. Peng Abstract. For integers p, q, s with p≥q≥2 and s≥0, let K2 - s(p,q) denote the set of 2 - connected bipartite graphs which can be obtained from Kp,q by deleting a set of s edges. In this paper, we prove that for any graph G∈K2 - 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 the similar theorem by Dong et al. [Discrete Math. 224(2000) 107–124], and the result in [4]. 2000 Mathematics Subject Classification: Primary 05C15. Full text: PDF