Chromatically Unique Bipartite Graphs with Certain 3-independent Partition Numbers II
نویسندگان
چکیده
Abstract. 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 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].
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Classes of chromatically unique graphs
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