Perfect One-Factorizations Arising from the Lee Metric

Let K n denote a complete graph on n vertices, where n is even. In recent works, geometric methods (finite projective planes, regular gons in the Euclidean plane) have been developed in the study of one-factorizations of K n , but a geometric viewpoint for perfect one-factorizations still remains un...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 39; no. 1
Main Authors Perondi, Pablo Henrique, Monte Carmelo, Emerson L.
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.02.2023
Springer Nature B.V
Subjects
Apexes
Combinatorics
Engineering Design
Euclidean geometry
Graph theory
Mathematics
Mathematics and Statistics
Original Paper
One-factorization
05C45
05C70
Perfect one-factorization
Complete graph
Lee metric
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Summary:Let K n denote a complete graph on n vertices, where n is even. In recent works, geometric methods (finite projective planes, regular gons in the Euclidean plane) have been developed in the study of one-factorizations of K n , but a geometric viewpoint for perfect one-factorizations still remains unknown. In this note we apply the Lee metric to construct a one-factorization of K 2 p for an odd number p , which is isomorphic to those factorizations by Anderson and by Nakamura. Moreover, this construction is perfect for an odd prime p . By combining our approach with previous results, some known maximum distance separable codes in the Hamming space can be derived from the Lee metric.
ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-022-02603-x