Perfect 2-colorings of Hamming graphs

被引：7

作者：

Bespalov, Evgeny A. ^{[1
]}

Krotov, Denis S. ^{[1
]}

Matiushev, Aleksandr A. ^{[2
]}

Taranenko, Anna A. ^{[1
]}

Vorob'ev, Konstantin V. ^{[1
]}

机构：

[1] Sobolev Inst Math, 4 Acad Koptyug Ave, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Novosibirsk, Russia

来源：

JOURNAL OF COMBINATORIAL DESIGNS | 2021年 / 29卷 / 06期

基金：

俄罗斯科学基金会;

关键词：

equitable partition; graph covering; Hamming graph; perfect code; perfect coloring; EQUITABLE PARTITIONS; ORTHOGONAL ARRAYS; BINARY-CODES; PARAMETERS; COLORINGS;

D O I：

10.1002/jcd.21771

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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).

引用

页码：367 / 396

页数：30

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