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Title: Chromatically unique bipartite graphs with low 3-independent partition numbers
Authors: Dong, F.M.
Koh, K.M. 
Teo, K.L.
Little, C.H.C.
Hendy, M.D.
Keywords: Bipartite graph
Chromatic polynomial
Issue Date: 28-Sep-2000
Source: Dong, F.M.,Koh, K.M.,Teo, K.L.,Little, C.H.C.,Hendy, M.D. (2000-09-28). Chromatically unique bipartite graphs with low 3-independent partition numbers. Discrete Mathematics 224 (1-3) : 107-124. ScholarBank@NUS Repository.
Abstract: For integers p,q,s with p≥q≥2 and s≥0, let script K sign-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 ∈ script K sign-s 2 (p,q) with p≥q≥3 and 1 ≤s≤q - 1, if the number of 3-independent partitions of G is at most 2p-1 + 2q-1 + s + 2, then G is χ-unique. It follows that any graph in script K sign-s 2 (p,q) is χ-unique if p≥q≥3 and 1 ≤s≤ {q - 1, 4}. © 2000 Elsevier Science B.V. All rights reserved.
Source Title: Discrete Mathematics
ISSN: 0012365X
Appears in Collections:Staff Publications

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