Perfect 2‐colorings of Hamming graphs. Issue 6 (10th March 2021)

• Record Type: Journal Article
• Authors: Bespalov, Evgeny A.; Krotov, Denis S.; Matiushev, Aleksandr A.; Taranenko, Anna A.; Vorob'ev, Konstantin V.
• Is Part Of: Journal of combinatorial designs. Volume 29:Issue 6(2021)
• Page Start: 367
• Page End: 396
• Publication Date: 2021-03-10
• Subjects: equitable partition -- graph covering -- Hamming graph -- perfect code -- perfect coloring; Combinatorial designs and configurations -- Periodicals; Configurations et schémas combinatoires -- Périodiques; 511.6
• DOI: 10.1002/jcd.21771
• Languages: English
• ISSNs: 1063-8539

Abstract

Abstract: 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).