A TIGHT BOUND ON THE SET CHROMATIC NUMBER

被引：2
|
作者：
Sereni, Jean-Sebastien [1 ]
Yilma, Zelealem B. [2 ]
机构：
[1] Univ Diderot, LORIA, CNRS, Nancy, France
[2] Addis Ababa Univ, Dept Math, Addis Ababa, Ethiopia
来源：
DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2013年 / 33卷 / 02期
关键词：
chromatic number; set coloring; set chromatic number; neighbor; distinguishing coloring;
D O I：
10.7151/dmgt.1679
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We provide a tight bound on the set chromatic number of a graph in terms of its chromatic number. Namely, for all graphs G, we show that chi(s)(G) equal to or greater than inverted right perpendicularlog(2) chi(G)inverted left perpendicular + 1, where chi(s)(G) and chi(G) are the set chromatic number and the chromatic number of G, respectively. This answers in the affirmative a conjecture of Gera, Okamoto, Rasmussen and Zhang.
引用
收藏
页码：461 / 465
页数：5
相关论文
共 50 条
  • [41] The chromatic number of ℝn with a set of forbidden distances
    A. B. Kupavskii
    Doklady Mathematics, 2010, 82 : 963 - 966
  • [42] The Chromatic Number of Rn with a Set of Forbidden Distances
    Kupavskii, A. B.
    DOKLADY MATHEMATICS, 2010, 82 (03) : 963 - 966
  • [43] ON CHROMATIC NUMBER OF FINITE SET-SYSTEMS
    LOVASZ, L
    ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1968, 19 (1-2): : 59 - &
  • [44] A tight upper bound on the number of candidate patterns
    Geerts, F
    Goethals, B
    Van den Bussche, J
    2001 IEEE INTERNATIONAL CONFERENCE ON DATA MINING, PROCEEDINGS, 2001, : 155 - 162
  • [45] Tight Bound for the Number of Distinct Palindromes in a Tree
    Gawrychowski, Pawel
    Kociumaka, Tomasz
    Rytter, Wojciech
    Walen, Tomasz
    ELECTRONIC JOURNAL OF COMBINATORICS, 2023, 30 (02):
  • [46] A Tight Bound for the Number of Edges of Matchstick Graphs
    Lavollee, Jeremy
    Swanepoel, Konrad
    DISCRETE & COMPUTATIONAL GEOMETRY, 2024, 72 (04) : 1530 - 1544
  • [47] Tight Bound for the Number of Distinct Palindromes in a Tree
    Gawrychowski, Pawel
    Kociumaka, Tomasz
    Rytter, Wojciech
    Walen, Tomasz
    STRING PROCESSING AND INFORMATION RETRIEVAL (SPIRE 2015), 2015, 9309 : 270 - 276
  • [48] Improved upper bound for acyclic chromatic number of graphs
    Cai, Jiansheng
    Wang, Jihui
    Yu, Jiguo
    ARS COMBINATORIA, 2019, 142 : 231 - 237
  • [49] AN UPPER BOUND FOR THE TOTAL CHROMATIC NUMBER OF DENSE GRAPHS
    HIND, HR
    JOURNAL OF GRAPH THEORY, 1992, 16 (03) : 197 - 203
  • [50] Vizing Bound for the Chromatic Number on Some Graph Classes
    T. Karthick
    Frédéric Maffray
    Graphs and Combinatorics, 2016, 32 : 1447 - 1460
12345