Near-proper vertex 2-colorings of sparse graphs

被引：1
|
作者：
Borodin O.V. [1 ]
Ivanova A.O. [2 ]
机构：
[1] Sobolev Institute of Mathematics, Novosibirsk, 630090
[2] Institute of Mathematics, Yakutsk State University, Yakutsk, 677891
来源：
Journal of Applied and Industrial Mathematics | 2010年 / 4卷 / 1期
基金：
俄罗斯基础研究基金会;
关键词：
Coloring; Girth; Partition; Planar graph;
D O I：
10.1134/S1990478910010047
中图分类号：
学科分类号：
摘要：
A graph G is (2, 1)-colorable if its vertices can be partitioned into subsets V1 and V2 such that each component in G[V1] contains at most two vertices while G[V2] is edgeless. We prove that every graph with maximum average degree mad(G) < 7/3 is (2, 1)-colorable. It follows that every planar graph with girth at least 14 is (2, 1)-colorable. We also construct a planar graph Gn with mad (Gn) = (18n - 2)/(7n - 1) that is not (2, 1)-colorable. © Pleiades Publishing, Ltd., 2010.
引用
收藏
页码：21 / 23
页数：2
相关论文
共 50 条
  • [1] Defective 2-colorings of sparse graphs
    Borodin, O. V.
    Kostochka, A. V.
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2014, 104 : 72 - 80
  • [2] Asymmetric 2-colorings of graphs
    Flapan, Erica
    Rundell, Sarah
    Wyse, Madeline
    [J]. JOURNAL OF GRAPH THEORY, 2017, 86 (04) : 361 - 374
  • [3] Proper interval vertex colorings of graphs
    Madaras, Tomáš
    Matisová, Daniela
    Onderko, Alfréd
    Šárošiová, Zuzana
    [J]. Applied Mathematics and Computation, 2024, 477
  • [4] 2-COLORINGS THAT DECOMPOSE PERFECT GRAPHS
    CHVATAL, V
    LENHART, WJ
    SBIHI, N
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1990, 49 (01) : 1 - 9
  • [5] Perfect 2-colorings of Hamming graphs
    Bespalov, Evgeny A.
    Krotov, Denis S.
    Matiushev, Aleksandr A.
    Taranenko, Anna A.
    Vorob'ev, Konstantin V.
    [J]. JOURNAL OF COMBINATORIAL DESIGNS, 2021, 29 (06) : 367 - 396
  • [6] 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
  • [7] Adjacent vertex distinguishing colorings by sum of sparse graphs
    Yu, Xiaowei
    Qu, Cunquan
    Wang, Guanghui
    Wang, Yiqiao
    [J]. DISCRETE MATHEMATICS, 2016, 339 (01) : 62 - 71
  • [8] On the vertex-distinguishing proper edge-colorings of graphs
    Bazgan, C
    Harkat-Benhamdine, A
    Li, H
    Wozniak, M
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 1999, 75 (02) : 288 - 301
  • [9] Perfect 2-Colorings of k-Regular Graphs
    Piri, Farzaneh
    Semnani, Saeed Mohammadian
    [J]. KYUNGPOOK MATHEMATICAL JOURNAL, 2020, 60 (02): : 349 - 359
  • [10] On the Number of k-Proper Connected Edge and Vertex Colorings of Graphs
    Barish, Robert D.
    [J]. THAI JOURNAL OF MATHEMATICS, 2023, 21 (04): : 917 - 936
12345