# Search results for: Xueliang Li

Bulletin of the Malaysian Mathematical Sciences Society > 2019 > 42 > 1 > 381-390

*P*in a total-colored graph

*G*is called a total-proper path if (1) any two adjacent edges of

*P*are assigned distinct colors; (2) any two adjacent internal vertices of

*P*are assigned distinct colors; and (3) any internal vertex of

*P*is assigned a distinct color from its incident edges of

*P*. The total-colored...

Bulletin of the Malaysian Mathematical Sciences Society > 2018 > 41 > 3 > 1199-1209

*P*in an edge-colored graph

*G*is called a proper path if no two adjacent edges of

*P*are colored the same, and

*G*is proper connected if every two vertices of

*G*are connected by a proper path in

*G*. The proper connection number of a connected graph

*G*, denoted by $$\textit{pc}(G)$$ pc(G) , is the minimum number of colors that are needed to make

*G*proper connected. In this paper, we investigate the...

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...