A lower bound for the length of a partial transversal in a Latin square

DOI10.1016/0097-3165(82)90074-7zbMath0489.05012OpenAlexW4239744687MaRDI QIDQ5905147

Peter W. Shor

Publication date: 1982

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

Full work available at URL: https://doi.org/10.1016/0097-3165(82)90074-7

zbMATH Keywords

Latin squares

Mathematics Subject Classification ID

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

Related Items (22)

The number of distinct symbols in sections of rectangular arrays ⋮ The number of transversals in a Latin square ⋮ Transversals in long rectangular arrays ⋮ New bounds for Ryser’s conjecture and related problems ⋮ Combinatorics. Abstracts from the workshop held January 1--7, 2023 ⋮ On a conjecture of Stein ⋮ Hamilton transversals in random Latin squares ⋮ Combinatorics, probability and computing. Abstracts from the workshop held April 24--30, 2022 ⋮ Balanced equi-\(n\)-squares ⋮ Orthogonal Latin Rectangles ⋮ Color degree and heterochromatic cycles in edge-colored graphs ⋮ Rainbow structures in locally bounded colorings of graphs ⋮ Rainbow matchings and cycle-free partial transversals of Latin squares ⋮ A lower bound for the length of a partial transversal in a Latin square ⋮ Rainbow matchings in bipartite multigraphs ⋮ Orthogonal matchings ⋮ A necessary and sufficient condition for the existence of a heterochromatic spanning tree in a graph ⋮ A matroid generalization of a result on row-Latin rectangles ⋮ Transversals in row-latin rectangles ⋮ Transversals in \(m \times n\) arrays ⋮ A NOTE ON RAINBOW MATCHINGS ⋮ Rainbow sets in the intersection of two matroids

Cites Work

• Unnamed Item
• An \(n\times n\) Latin square has a transversal with at least \(n-\sqrt n\) distinct symbols
• Maximal sets of Latin squares and partial transversals
• A lower bound for the order of a partial transversal in a latin square

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