Perfect 2‐colorings of Hamming graphs Full article
| Journal |
Journal of Combinatorial Designs
ISSN: 1063-8539 |
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| Output data | Year: 2021, Volume: 29, Number: 6, Pages: 367-396 Pages count : 30 DOI: 10.1002/jcd.21771 | ||||
| Tags | equitable partition, graph covering, Hamming graph, perfect code, perfect coloring | ||||
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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 for small and . Using the connection with perfect colorings, we construct an orthogonal array A(2048, 7, 4, 5).
Cite:
Bespalov E.A.
, Krotov D.S.
, Matiushev A.A.
, Taranenko A.A.
, Vorob'ev K.V.
Perfect 2‐colorings of Hamming graphs
Journal of Combinatorial Designs. 2021. V.29. N6. P.367-396. DOI: 10.1002/jcd.21771 WOS Scopus РИНЦ OpenAlex
Perfect 2‐colorings of Hamming graphs
Journal of Combinatorial Designs. 2021. V.29. N6. P.367-396. DOI: 10.1002/jcd.21771 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Feb 16, 2020 |
| Accepted: | Feb 8, 2021 |
| Published online: | Mar 10, 2021 |
Identifiers:
| Web of science: | WOS:000627028000001 |
| Scopus: | 2-s2.0-85102249444 |
| Elibrary: | 46806514 |
| OpenAlex: | W3133704031 |