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- Title
Reconfiguring k-colourings of Complete Bipartite Graphs.
- Authors
CELAYA, MARCEL; CHOO, KELLY; MACGILLIVRAY, GARY; SEYFFARTH, KAREN
- Abstract
Let H be a graph, and k ≥Χ(H) an integer. We say that H has a cyclic Gray code of k-colourings if and only if it is possible to list all its k-colourings in such a way that consecutive colourings, including the last and the first, agree on all vertices of H except one. The Gray code number of H is the least integer k0(H) such that H has a cyclic Gray code of its k-colourings for all k ≥ k0(H). For complete bipartite graphs, we prove that k0(Kℓ,r) = 3 when both ℓ and r are odd, and k0(Kℓ,r) = 4 otherwise.
- Subjects
BIPARTITE graphs; GRAY codes; INTEGERS; ODD numbers; GEOMETRIC vertices; MATHEMATICAL proofs
- Publication
Kyungpook Mathematical Journal, 2016, Vol 56, Issue 3, p647
- ISSN
1225-6951
- Publication type
Article
- DOI
10.5666/KMJ.2016.56.3.647