Chromatically Unique Bipartite Graphs with Certain 3-independent Partition Numbers - Hasni, Roslan; Peng, Y.H. (MATEMATIKA, 2006)
For integers p, q, s with pq2 and s0, let K_2^-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 GK_2^-s(p,q) with pq3 and 1sq-1, if the number of 3-independent partitions of G is 2^p-1+2^q-1+s+3, then G is chromatically unique. This result extends the similar theorem by Dong et al. (Discrete Math. vol. 224 (2000) 107–124). Keywords: Chromatic polynomial; chromatically equivalence; chromatically unique.