The perfect colorings of circulant graphs with a large number of colors

被引：0
|
作者：
Lisitsyna, Mariya Aleksandrovna [1 ]
Avgustinovich, Sergey Vladimirovich [2 ]
机构：
[1] Mozhaisky Mil Space Acad, Zhdanovskaya 13, St Petersburg 197198, Russia
[2] Sobolev Inst Math, Pr Koptyuga 4, Novosibirsk 630090, Russia
来源：
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2024年 / 21卷 / 01期
关键词：
perfect coloring; infinite circulant graph; k-motley fragment;
D O I：
10.33048/semi.2024.21.013
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
An infinite circulant graph with a continuous set of distances is a graph, whose set of vertices is the set of integers, and two vertices i and j are adjacent if |i - j| is an element of{1, 2, . . . , n}. We study perfect colorings of such graph with k colors for k at least 3n + 3. A complete description of them is obtained.
引用
收藏
页码：188 / 195
页数：8
相关论文
共 50 条
  • [41] On the clique number of integral circulant graphs
    Basic, Milan
    Ilic, Aleksandar
    APPLIED MATHEMATICS LETTERS, 2009, 22 (09) : 1406 - 1411
  • [42] The Number of Defective Colorings of Graphs on Surfaces
    Rackham, Tom
    JOURNAL OF GRAPH THEORY, 2011, 68 (02) : 129 - 136
  • [43] Linear Alexander quandle colorings and the minimum number of colors
    Elhamdadi, Mohamed
    Kerr, Jeremy
    KNOTS, LINKS, SPATIAL GRAPHS, AND ALGEBRAIC INVARIANTS, 2017, 689 : 7 - 22
  • [44] The number of rooted forests in circulant graphs
    Grunwald, Lilya A.
    Mednykh, Ilya
    ARS MATHEMATICA CONTEMPORANEA, 2022, 22 (04)
  • [45] On the chromatic number of integral circulant graphs
    Ilic, Aleksandar
    Basic, Milan
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (01) : 144 - 150
  • [46] Perfect 2-colorings of transitive cubic graphs
    Avgustinovich S.V.
    Lisitsyna M.A.
    Journal of Applied and Industrial Mathematics, 2011, 5 (4) : 519 - 528
  • [47] Perfect graphs of arbitrarily large clique-chromatic number
    Charbit, Pierre
    Penev, Irena
    Thomasse, Stephan
    Trotignon, Nicolas
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2016, 116 : 456 - 464
  • [48] On The Defining Number For Vertex Colorings Of A Family Of Graphs
    Sharebaf, Sadegh Rahimi
    Rad, Nader Jafari
    APPLIED MATHEMATICS E-NOTES, 2011, 11 : 118 - 124
  • [49] On the number of spanning trees in directed circulant graphs
    Lonc, Z
    Parol, K
    Wojciechowski, JM
    NETWORKS, 2001, 37 (03) : 129 - 133
  • [50] The formulas for the number of spanning trees in circulant graphs
    Li, Min
    Chen, Zhibing
    Ruan, Xiaoqing
    Yong, Xuerong
    DISCRETE MATHEMATICS, 2015, 338 (11) : 1883 - 1906
12345