Switching in one-factorisations of complete graphs

zbMath1300.05254MaRDI QIDQ405262

Patric R. J. Östergård, Petteri Kaski, André de Souza Medeiros, Ian M. Wanless

Publication date: 4 September 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i2p49

zbMATH Keywords

group divisible designswitchingatomic Latin squareHamiltonian Latin squareone-factorisationperfect one-factorisation

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60) Graph designs and isomorphic decomposition (05C51)

Related Items (9)

One-factorisations of complete graphs arising from ovals in finite planes ⋮ Parity of sets of mutually orthogonal Latin squares ⋮ Perfect one-factorizations arising from the Lee metric ⋮ Enumeration of Latin squares with conjugate symmetry ⋮ Efficient, local and symmetric Markov chains that generate one-factorizations ⋮ Parity of transversals of Latin squares ⋮ Recoloring subgraphs of \(K_{2n}\) for sports scheduling ⋮ Latin Squares with a Unique Intercalate ⋮ PERFECT 1-FACTORISATIONS OF

Uses Software

• nauty
• Traces

Cites Work

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• Generating uniformly distributed random latin squares
• Atomic Latin squares of order eleven
• Symmetries that latin squares inherit from 1‐factorizations
• There are 526,915,620 nonisomorphic one‐factorizations of K₁₂

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