Rainbow Connection Number of Graphs with Diameter 3

Hengzhe Li, Xueliang Li, and Yuefang Sun. "Rainbow Connection Number of Graphs with Diameter 3." Discussiones Mathematicae Graph Theory 37.1 (2017): 141-154. <http://eudml.org/doc/288080>.

@article{HengzheLi2017,
abstract = {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.},
author = {Hengzhe Li, Xueliang Li, Yuefang Sun},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge-coloring; rainbow path; rainbow connection number; diameter; edge coloring},
language = {eng},
number = {1},
pages = {141-154},
title = {Rainbow Connection Number of Graphs with Diameter 3},
url = {http://eudml.org/doc/288080},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Hengzhe Li
AU - Xueliang Li
AU - Yuefang Sun
TI - Rainbow Connection Number of Graphs with Diameter 3
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 1
SP - 141
EP - 154
AB - 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.
LA - eng
KW - edge-coloring; rainbow path; rainbow connection number; diameter; edge coloring
UR - http://eudml.org/doc/288080
ER -