# Search results for: Xueliang Li

Bulletin of the Malaysian Mathematical Sciences Society > 2017 > 40 > 4 > 1769-1779

*monochromatically-connecting coloring*(MC-coloring, for short) if there is a monochromatic path joining any two vertices, which was introduced by Caro and Yuster. Let

*mc*(

*G*) denote the maximum number of colors used in an MC-coloring of a graph

*G*. Note that an MC-coloring does not exist if

*G*is not connected, in which case we simply let $$mc(G)=0$$ mc(G)=0...

Discrete Mathematics > 2015 > 338 > 5 > 669-673

Linear Algebra and Its Applications > 2015 > 465 > Complete > 283-295

Graphs and Combinatorics > 2013 > 29 > 5 > 1471-1475

*G*is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph

*G*, denoted by

*rc*(

*G*), is the smallest number of colors that are needed in order to make

*G*rainbow connected. In this paper, we proved that

*rc*(

*G*) ≤ 3(

*n*+ 1)/5 for all 3-connected graphs.

Discrete Mathematics > 2010 > 310 > 15-16 > 2147-2163