Perfect 2‐colorings of Hamming graphs

We consider the problem of existence of perfect 2‐colorings (equitable 2‐partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs and colorings that are necessary for their existence. Next we observe known constructions of perfect colorings and propose so...

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Bibliographic Details
Published inJournal of combinatorial designs Vol. 29; no. 6; pp. 367 - 396
Main Authors Bespalov, Evgeny A., Krotov, Denis S., Matiushev, Aleksandr A., Taranenko, Anna A., Vorob'ev, Konstantin V.
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc 01.06.2021
Subjects
equitable partition
graph covering
Graphs
Hamming graph
Orthogonal arrays
Parameters
perfect code
perfect coloring
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Summary:We consider the problem of existence of perfect 2‐colorings (equitable 2‐partitions) of Hamming graphs with given parameters. We start with conditions on parameters of graphs and colorings that are necessary for their existence. Next we observe known constructions of perfect colorings and propose some new ones giving new parameters. At last, we deduce which parameters of colorings are covered by these constructions and give tables of admissible parameters of 2‐colorings in Hamming graphs H ( n , q ) for small n and q. Using the connection with perfect colorings, we construct an orthogonal array OA(2048, 7, 4, 5).
ISSN:1063-8539
1520-6610
DOI:10.1002/jcd.21771