# Search results for: Xueliang Li

Discussiones Mathematicae Graph Theory > 2017 > 37 > 1 > 141-154

Graphs and Combinatorics > 2016 > 32 > 5 > 1829-1841

*G*, the minimum number of colors that are needed to make

*G*rainbow connected is called the rainbow connection number of

*G*, denoted by rc(

*G*). In this paper,...

Graphs and Combinatorics > 2015 > 31 > 1 > 141-147

*G*is

*rainbow connected*if every pair of vertices of

*G*are connected by a path whose edges have distinct colors. The

*rainbow connection number*

*rc*(

*G*) of

*G*is defined to be the minimum integer

*t*such that there exists an edge-coloring of

*G*with

*t*colors that makes

*G*rainbow connected. For a graph

*G*without any cut vertex, i.e., a 2-connected graph, of order

*n*, it was proved that...

Graphs and Combinatorics > 2014 > 30 > 4 > 949-955

*G*, where adjacent edges may have the same color, is

*rainbow connected*if every two vertices of

*G*are connected by a path whose edges have distinct colors. A graph

*G*is

*d-rainbow connected*if one can use

*d*colors to make

*G*rainbow connected. For integers

*n*and

*d*let

*t*(

*n, d*) denote the minimum size (number of edges) in

*d*-rainbow connected graphs of order

*n*. Schiermeyer got some...

Discussiones Mathematicae Graph Theory > 2013 > 33 > 3 > 603-611

Graphs and Combinatorics > 2013 > 29 > 5 > 1235-1247

*G*is

*rainbow connected*if every two vertices of

*G*are connected by a path whose edges have distinct colors. The

*rainbow connection number*of

*G*, denoted by

*rc*(

*G*), is the minimum number of colors that are needed to make

*G*rainbow connected. In this paper we give a Nordhaus–Gaddum-type result for the rainbow connection number. We prove that if

*G*and $${\overline{G}}$$ are both...

Graphs and Combinatorics > 2013 > 29 > 6 > 1733-1739

*G*be a connected graph. The notion of rainbow connection number

*rc*(

*G*) of a graph

*G*was introduced by Chartrand et al. (Math Bohem 133:85–98, 2008). Basavaraju et al. (arXiv:1011.0620v1 [math.CO], 2010) proved that for every bridgeless graph

*G*with radius

*r*, $${rc(G)\leq r(r+2)}$$ and the bound is tight. In this paper, we show that for a connected graph

*G*with radius

*r*and center vertex

*u*,...

Discrete Mathematics > 2012 > 312 > 8 > 1453-1457

Graphs and Combinatorics > 2012 > 28 > 2 > 251-263

*G*, where adjacent edges may be colored the same, is called a rainbow path if no two edges of it are colored the same. A nontrivial connected graph

*G*is rainbow connected if for any two vertices of

*G*there is a rainbow path connecting them. The rainbow connection number of

*G*, denoted

*rc*(

*G*), is defined as the smallest number of colors such that

*G*is rainbow connected...