A solution of Dudeney's round table problem for an even number of people
type: Item
instance of: scholarly article
title: A solution of Dudeney's round table problem for an even number of people
zbMATH Open document ID: 0783.05033
DOI: 10.1016/0097-3165(93)90022-Z
author: Midori Kobayashi
author: Kiyasu-Zen'iti
author: Gisaku Nakamura
published in: Journal of Combinatorial Theory. Series A
publication date: 1993-05-23T00:00:00Z
review text: In 1905 \textit{H. E. Dudeney} [Amusements in Mathematics, Nelson, Lord, 1917; Dover reprint, New York, 1970] asked if \(n\) people could be seated at a round table on \((n-1)\) \((n-2)/2\) consecutive days so that no person would have the same pair of neighbors more than once. Equivalently, this asks for a family of Hamilton cycles in \(K_ n\) so that every 2-path is on exactly one cycle. In this paper the authors provide constructions of these families for all even \(n\). The case when \(n\) is odd is far more difficult and few results are known.
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C70
zbMATH DE Number: 165156
zbMATH Keywords: complete graph
zbMATH Keywords: round table
zbMATH Keywords: Hamilton cycles
zbMATH Keywords: 2-path
reviewed by: Katherine Heinrich
MaRDI profile type: Publication
cites work: Symmetry groups of some perfect 1-factorizations of complete graphs
cites work: Dudeney's round table problem
cites work: Exact coverings of 2-paths by 4-cycles
cites work: A perfect one-factorization of \(K_{36}\)
cites work: Exact coverings of 2-paths by Hamilton cycles
cites work: Resolvable coverings of 2-paths by 4-cycles
cites work: Q3874209
full work available at URL: 0097-3165(93)90022-z
OpenAlex ID: W2021048097
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description: scientific article; zbMATH DE number 165156