Clique decompositions of multipartite graphs and completion of Latin squares

DOI10.1016/j.jcta.2017.04.005zbMath1366.05018arXiv1603.01043OpenAlexW2963159358MaRDI QIDQ2363362

Allan Lo, Deryk Osthus, Ben Barber, Amelia Taylor, Daniela Kühn

Publication date: 13 July 2017

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.01043

zbMATH Keywords

mutually orthogonal Latin squaresedge decompositions

Mathematics Subject Classification ID

Orthogonal arrays, Latin squares, Room squares (05B15)

Related Items (14)

The Existence of Designs via Iterative Absorption: Hypergraph 𝐹-designs for Arbitrary 𝐹 ⋮ Restricted extension of sparse partial edge colorings of complete graphs ⋮ Embedding partial Latin squares in Latin squares with many mutually orthogonal mates ⋮ Fractional clique decompositions of dense graphs and hypergraphs ⋮ Substructures in Latin squares ⋮ Restricted extension of sparse partial edge colorings of hypercubes ⋮ Completion and deficiency problems ⋮ Minimalist designs ⋮ Fractional Clique Decompositions of Dense Partite Graphs ⋮ Edge-decompositions of graphs with high minimum degree ⋮ A lower bound on HMOLS with equal sized holes ⋮ Restricted completion of sparse partial Latin squares ⋮ On the decomposition threshold of a given graph ⋮ Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results

Cites Work

• Corrigendum to ``Rational decomposition of dense hypergraphs and some related eigenvalue estimates
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• Asymptotically optimal \(K_k\)-packings of dense graphs via fractional \(K_k\)-decompositions
• Completions of ε-Dense Partial Latin Squares
• Thank Evans!
• On the Maximal Number of Pairwise Orthogonal Latin Squares of a Given Order
• Fractional Triangle Decompositions in Graphs with Large Minimum Degree
• Integer and fractional packing of families of graphs
• A Multipartite Version of the Hajnal–Szemerédi Theorem for Graphs and Hypergraphs
• Edge-disjoint Hamilton cycles in random graphs
• Fractional Clique Decompositions of Dense Partite Graphs
• Edge-decompositions of graphs with high minimum degree
• A generalization of transversals for Latin squares
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