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dc.contributor.authorCavenagh, Nicholas J.en_NZ
dc.contributor.authorDonovan, Diane M.en_NZ
dc.contributor.authorYazıcı, Emine S.en_NZ
dc.date.accessioned2020-10-01T22:48:39Z
dc.date.available2020-10-01T22:48:39Z
dc.date.issued2020en_NZ
dc.identifier.citationCavenagh, N. J., Donovan, D. M., & Yazıcı, E. S. (2020). Biembeddings of cycle systems using integer Heffter arrays. Journal of Combinatorial Designs, 1–23. https://doi.org/10.1002/jcd.21753en
dc.identifier.issn1063-8539en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/13866
dc.description.abstractIn this paper, we use constructions of Heffter arrays to verify the existence of face 2‐colorable embeddings of cycle decompositions of the complete graph. Specifically, for n ≡ 1 (mod 4) and k ≡3(mod 4), n k ≫ ⩾ 7 and when n ≡ 0(mod 3) then k ≡ 7(mod 12), there exist face 2-colorable embeddings of the complete graph K₂ₙₖ₊₁ onto an orientable surface where each face is a cycle of a fixed length k. In these embeddings the vertices of K₂ₙₖ₊₁ will be labeled with the elements of Z₂ₙₖ₊₁ in such a way that the group, (Z₂ₙₖ₊₁, +) acts sharply transitively on the vertices of the embedding. This result is achieved by verifying the existence of nonequivalent Heffter arrays, H (n ; k), which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo 2nk + 1; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arrays H (n ; k) that satisfy condition (1) was established earlier in Burrage et al. and in this current paper, we vary this construction and show, for k ⩾ 11, that there are at least (n − 2)[((k − 11)/4)!/ ]² such nonequivalent H (n ; k) that satisfy both conditions (1) and (2).
dc.language.isoenen_NZ
dc.publisherWileyen_NZ
dc.rightsThis is an author's accepted version of an article published in Journal of Combinatorial designs. ©2020 Wiley.
dc.subjectmathematicsen_NZ
dc.subjectbiembedding cycle systemsen_NZ
dc.subjectHeffter arrayen_NZ
dc.titleBiembeddings of cycle systems using integer Heffter arraysen_NZ
dc.typeJournal Article
dc.identifier.doi10.1002/jcd.21753en_NZ
dc.relation.isPartOfJournal of Combinatorial Designsen_NZ
pubs.begin-page1
pubs.elements-id257537
pubs.end-page23
pubs.publication-statusPublished onlineen_NZ
dc.identifier.eissn1520-6610en_NZ


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