ON A METRIC PROPERTY OF PERFECT COLORINGS

被引：0
|
作者：
Taranenko, A. A. [1 ]
机构：
[1] Sobolev Inst Math, 4 Koptyuga Ave, Novosibirsk 630090, Russia
来源：
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2021年 / 18卷
关键词：
perfect coloring; perfect structure; L-1; distance; circulant graph; square grid; triangular grid;
D O I：
10.33048/semi.2021.18.046
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a perfect coloring of a graph, we prove that the L-1 distance between two rows of the adjacency matrix of the graph is not less than the L-1 distance between the corresponding rows of the parameter matrix of the coloring. With the help of an algebraic approach, we deduce corollaries of this result for perfect 2-colorings and perfect colorings in distance-l graphs and distance-regular graphs. We also provide examples of infinite graphs, where the obtained property rejects several putative parameter matrices of perfect colorings.
引用
收藏
页码：640 / 646
页数：7
相关论文
共 50 条
  • [1] On a metric property of perfect colorings
    Sobolev Institute of Mathematics, Novosibirsk, Russia
    [J]. arXiv,
  • [2] PERFECT COLORINGS
    BROWN, JI
    CORNEIL, DG
    [J]. ARS COMBINATORIA, 1990, 30 : 141 - 159
  • [3] PERFECT AND LOCALLY - PERFECT COLORINGS
    RUSU, I
    [J]. JOURNAL OF GRAPH THEORY, 1995, 20 (04) : 501 - 512
  • [4] Perfect colorings of hypergraphs
    Sobolev Institute of Mathematics, Novosibirsk, Russia
    [J]. arXiv, 1600,
  • [5] INDUCED PERFECT COLORINGS
    Avgustinovich, S. V.
    Mogilnykh, I. Yu.
    [J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2011, 8 : 310 - 316
  • [6] ECOLOGICAL AND PERFECT COLORINGS
    BORGATTI, SP
    EVERETT, MG
    [J]. SOCIAL NETWORKS, 1994, 16 (01) : 43 - 55
  • [7] PERFECT COLORINGS OF MULTIPATTERNS IN THE PLANE
    ROTH, RL
    [J]. DISCRETE MATHEMATICS, 1993, 122 (1-3) : 269 - 286
  • [8] Perfect colorings of the prism graph
    Lisitsyna, Mariya Aleksandrovna
    Avgustinovich, Sergey Vladimirovich
    [J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2016, 13 : 1116 - 1128
  • [9] On Forced Periodicity of Perfect Colorings
    Herva, Pyry
    Kari, Jarkko
    [J]. THEORY OF COMPUTING SYSTEMS, 2023, 67 (04) : 732 - 759
  • [10] Sequential colorings and perfect graphs
    Maffray, F
    Preissmann, M
    [J]. DISCRETE APPLIED MATHEMATICS, 1999, 94 (1-3) : 287 - 296
12345