Chromatic Uniqueness of Complete Bipartite Graphs With Certain Edges Deleted

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 Kp,q by deleting a set of s edges. In this paper, we prove that for any graph G ∈ K−s 2 (p, q) with p ≥ q ≥ 3, if 11 ≤ s ≤ q − 1 and ∆(G′) = s − 4, where G′ = Kp,q − G, then G is chromatically unique. This result extends both a theorem by Dong et al. [2] and the result in [4]. AMS (MOS) Subject Classification Codes: 05C15