# Search results for: Xueliang Li

Bulletin of the Malaysian Mathematical Sciences Society > 2016 > 39 > 1 > 409-425

*G*be an edge-colored graph. A rainbow (heterochromatic, or multicolored) path of

*G*is such a path in which no two edges have the same color. Let the color degree of a vertex

*v*to be the number of different colors that are used on edges incident to

*v*, and denote it by $$d^c(v)$$ d c ( v ) . In a previous paper, we showed that if $$d^c(v)\ge k$$ d c ( v ) ≥ k (color...

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*,...

Applied Mathematics Letters > 2009 > 22 > 10 > 1525-1528

Discrete Mathematics > 2009 > 309 > 10 > 3370-3380

Graphs and Combinatorics > 2008 > 24 > 4 > 237-263