RAINBOW CONNECTION NUMBER OF GRAPHS WITH DIAMETER 3

被引：10
|
作者：
Li, Hengzhe [1 ]
Li, Xueliang
Sun, Yuefang
机构：
[1] Nankai Univ, Ctr Combinator, Tianjin 300071, Peoples R China
来源：
DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2017年 / 37卷 / 01期
关键词：
edge-coloring; rainbow path; rainbow connection number; diameter;
D O I：
10.7151/dmgt.1920
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A path in an edge-colored graph G is rainbow if no two edges of the path are colored the same. The rainbow connection number rc(G) of G is the smallest integer k for which there exists a k-edge-coloring of G such that every pair of distinct vertices of G is connected by a rainbow path. Let f(d) denote the minimum number such that rc(G) <= f(d) for each bridgeless graph G with diameter d. In this paper, we shall show that 7 <= f (3) <= 9.
引用
收藏
页码：141 / 154
页数：14
相关论文
共 50 条
  • [41] Generalized Rainbow Connection of Graphs
    Zhu, Xiaoyu
    Wei, Meiqin
    Magnant, Colton
    BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2021, 44 (06) : 3991 - 4002
  • [42] Generalized Rainbow Connection of Graphs
    Xiaoyu Zhu
    Meiqin Wei
    Colton Magnant
    Bulletin of the Malaysian Mathematical Sciences Society, 2021, 44 : 3991 - 4002
  • [43] Rainbow connection in oriented graphs
    Dorbec, Paul
    Schiermeyer, Ingo
    Sidorowicz, Elzbieta
    Sopena, Eric
    DISCRETE APPLIED MATHEMATICS, 2014, 179 : 69 - 78
  • [44] RAINBOW CONNECTION IN SPARSE GRAPHS
    Kemnitz, Arnfried
    Przybylo, Jakub
    Schiermeyer, Ingo
    Wozniak, Mariusz
    DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2013, 33 (01) : 181 - 192
  • [45] Rainbow Connection Number and the Number of Blocks
    Xueliang Li
    Sujuan Liu
    Graphs and Combinatorics, 2015, 31 : 141 - 147
  • [46] Rainbow Connection Number and the Number of Blocks
    Li, Xueliang
    Liu, Sujuan
    GRAPHS AND COMBINATORICS, 2015, 31 (01) : 141 - 147
  • [47] GRAPHS OF DIAMETER 3 WITH THE MINIMUM NUMBER OF EDGES
    FUREDI, Z
    GRAPHS AND COMBINATORICS, 1990, 6 (04) : 333 - 337
  • [48] Rainbow Connection Number and Radius
    Manu Basavaraju
    L. Sunil Chandran
    Deepak Rajendraprasad
    Arunselvan Ramaswamy
    Graphs and Combinatorics, 2014, 30 : 275 - 285
  • [49] Rainbow Connection Number and Radius
    Basavaraju, Manu
    Chandran, L. Sunil
    Rajendraprasad, Deepak
    Ramaswamy, Arunselvan
    GRAPHS AND COMBINATORICS, 2014, 30 (02) : 275 - 285
  • [50] Rainbow Connection Number and Connectivity
    Li, Xueliang
    Liu, Sujuan
    Chandran, L. Sunil
    Mathew, Rogers
    Rajendraprasad, Deepak
    ELECTRONIC JOURNAL OF COMBINATORICS, 2012, 19 (01):
12345