# Search results for: Xueliang Li

Graphs and Combinatorics > 2017 > 33 > 4 > 999-1008

*G*is called

*a rainbow tree*if no two edges of it are assigned the same color. For a vertex subset $$S\subseteq V(G)$$ S ⊆ V ( G ) , a tree is called an

*S*-

*tree*if it connects

*S*in

*G*. A

*k*-

*rainbow coloring*of

*G*is an edge-coloring of

*G*having the property that for every set

*S*of

*k*vertices of

*G*, there exists a rainbow

*S*-tree in

*G*. The minimum number...

Discrete Applied Mathematics > 2016 > 209 > C > 68-74

Discussiones Mathematicae Graph Theory > 2015 > 35 > 1 > 81-94

*G*was introduced by Chartrand et al. (Network 54(2) (2009), 75–81; 55 (2010), 360–367). For the complete graph

*K*

_{n}of order $n\ge 6$, they showed that $r{x}_{3,\ell}\left({K}_{n}\right)=3$ for $\ell =1,2$. Furthermore, they conjectured that for every positive integer $\ell $, there exists a positive integer

*N*such that $r{x}_{3,\ell}\left({K}_{n}\right)=3$ for every integer $n\ge N$. More generally, they conjectured that for every...