# Search results for: Xueliang Li

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

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*...