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

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 k(p,q) by deleting a set of s edges. in this paper, we prove that for any graph gєk2 − 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]