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
  • [31] The rainbow vertex connection number of edge corona product graphs
    Fauziah, D. A.
    Dafik
    Agustin, I. H.
    Alfarisi, R.
    FIRST INTERNATIONAL CONFERENCE ON ENVIRONMENTAL GEOGRAPHY AND GEOGRAPHY EDUCATION (ICEGE), 2019, 243
  • [32] RAINBOW CONNECTION IN GRAPHS
    Chartrand, Gary
    Johns, Garry L.
    McKeon, Kathleen A.
    Zhang, Ping
    MATHEMATICA BOHEMICA, 2008, 133 (01): : 85 - 98
  • [33] Rainbow Connection in 3-Connected Graphs
    Xueliang Li
    Yongtang Shi
    Graphs and Combinatorics, 2013, 29 : 1471 - 1475
  • [34] Rainbow Connection in 3-Connected Graphs
    Li, Xueliang
    Shi, Yongtang
    GRAPHS AND COMBINATORICS, 2013, 29 (05) : 1471 - 1475
  • [35] Some upper bounds for the total-rainbow connection number of graphs
    Liu, Sujuan
    Zhao, Yan
    Wang, Linlin
    ARS COMBINATORIA, 2020, 150 : 159 - 169
  • [36] Nordhaus–Gaddum-Type Theorem for Rainbow Connection Number of Graphs
    Lily Chen
    Xueliang Li
    Huishu Lian
    Graphs and Combinatorics, 2013, 29 : 1235 - 1247
  • [37] On the Locating Rainbow Connection Number of the Comb Product with Complete Graphs or Trees
    Imrona, Mahmud
    Salman, A. N. M.
    Uttunggadewa, Saladin
    Putri, Pritta Etriana
    COMBINATORICS, GRAPH THEORY AND COMPUTING, SEICCGTC 2021, 2024, 448 : 203 - 214
  • [38] Further hardness results on the rainbow vertex-connection number of graphs
    Chen, Lily
    Li, Xueliang
    Lian, Huishu
    THEORETICAL COMPUTER SCIENCE, 2013, 481 : 18 - 23
  • [39] Nordhaus-Gaddum-Type Theorem for Rainbow Connection Number of Graphs
    Chen, Lily
    Li, Xueliang
    Lian, Huishu
    GRAPHS AND COMBINATORICS, 2013, 29 (05) : 1235 - 1247
  • [40] Rainbow connections for outerplanar graphs with diameter 2 and 3
    Huang, Xiaolong
    Li, Xueliang
    Shi, Yongtang
    Yue, Jun
    Zhao, Yan
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 242 : 277 - 280
12345