Chromatically Unique Bipartite Graphs with Certain 3-independent Partition Numbers II

For integers p, q, s with p≥ q ≥2 and s≥ 0, let K_s ^2 (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 G Є K_2^-s (p, q) with p≥ q ≥3 and 1 ≤ s ≤ q-1, if the number of 3-independent partitions of G is 2^p-1 + 2^q-1 + s + 4, then G is chromatically unique. This result extends the similar theorem by Dong et al.