# Search results for: Xueliang Li

Graphs and Combinatorics > 2018 > 34 > 6 > 1553-1563

*G*is

*conflict-free connected*if every two of its vertices are connected by a path, which contains a color used on exactly one of its edges. The

*conflict-free connection number*of a connected graph

*G*, denoted by

*cfc*(

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

*G*conflict-free connected. For a graph

*G*, let

*C*(

*G*) be the subgraph of

*G*induced by its set of cut-edges...

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

Bulletin of the Malaysian Mathematical Sciences Society > 2018 > 41 > 4 > 1681-1695

*T*in an edge-colored graph is a

*proper tree*if no two adjacent edges of

*T*receive the same color. Let

*G*be a connected graph of order

*n*and

*k*be a fixed integer with $$2\le k\le n$$ 2≤k≤n . For a vertex subset $$S \subseteq V(G)$$ S⊆V(G) with $$\left| S\right| \ge 2$$ S≥2 , a tree containing all the vertices of

*S*in

*G*is called an

*S*-tree. An edge-coloring of

*G*is called a

*k*-

*proper coloring*...

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...

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

Computers and Mathematics with Applications > 2011 > 62 > 11 > 4082-4088

Discrete Mathematics > 2009 > 309 > 8 > 2575-2578

Discrete Mathematics > 2008 > 308 > 17 > 3871-3878

Discussiones Mathematicae Graph Theory > 1997 > 17 > 2 > 259-269