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
收藏
页码：367 / 396
页数：30
相关论文
共 50 条
  • [1] 2-COLORINGS THAT DECOMPOSE PERFECT GRAPHS
    CHVATAL, V
    LENHART, WJ
    SBIHI, N
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1990, 49 (01) : 1 - 9
  • [2] Perfect 2-colorings of transitive cubic graphs
    Avgustinovich S.V.
    Lisitsyna M.A.
    [J]. Journal of Applied and Industrial Mathematics, 2011, 5 (4) : 519 - 528
  • [3] Perfect 2-Colorings of k-Regular Graphs
    Piri, Farzaneh
    Semnani, Saeed Mohammadian
    [J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2020, 60 (02): : 349 - 359
  • [4] Perfect 2-colorings of a hypercube
    D. G. Fon-Der-Flaass
    [J]. Siberian Mathematical Journal, 2007, 48 : 740 - 745
  • [5] ON PERFECT 2-COLORINGS OF THE HYPERCUBE
    Vorobev, K. V.
    Fon-Der-Flaass, D. G.
    [J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2010, 7 : 65 - 75
  • [6] Perfect 2-colorings of a hypercube
    Fon-Der-Flaass, D. G.
    [J]. SIBERIAN MATHEMATICAL JOURNAL, 2007, 48 (04) : 740 - 745
  • [7] Asymmetric 2-colorings of graphs
    Flapan, Erica
    Rundell, Sarah
    Wyse, Madeline
    [J]. JOURNAL OF GRAPH THEORY, 2017, 86 (04) : 361 - 374
  • [8] Defective 2-colorings of sparse graphs
    Borodin, O. V.
    Kostochka, A. V.
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2014, 104 : 72 - 80
  • [9] Perfect 2-colorings of infinite circulant graphs with continuous set of distances
    Parshina O.G.
    [J]. Journal of Applied and Industrial Mathematics, 2014, 8 (3) : 357 - 361
  • [10] Perfect 2-colorings of the cubic graphs of order less than or equal to 10
    Alaeiyan, Mehdi
    Mehrabani, Ayoob
    [J]. AKCE INTERNATIONAL JOURNAL OF GRAPHS AND COMBINATORICS, 2020, 17 (01) : 380 - 386
12345