相关论文: Nordhaus-Gaddum-type theorem for rainbow connectio…
A vertex-colored graph $G$ is rainbow vertex-connected if any pair of distinct vertices are connected by a path whose internal vertices have distinct colors. The rainbow vertex-connection number of $G$, denoted by $rvc(G)$, is the minimum…
A graph is said to be \emph{total-colored} if all the edges and the vertices of the graph are colored. A total-colored graph is \emph{total-rainbow connected} if any two vertices of the graph are connected by a path whose edges and internal…
An edge-cut $R$ of an edge-colored connected graph is called a rainbow-cut if no two edges in the edge-cut are colored the same. An edge-colored graph is rainbow disconnected if for any two distinct vertices $u$ and $v$ of the graph, there…
Let $G$ be a nontrivial edge-colored connected graph. An edge-cut $R$ of $G$ is called a rainbow cut if no two edges of it are colored the same. An edge-colored graph $G$ is rainbow disconnected if for every two vertices $u$ and $v$, there…
An edge-colored graph $G$ 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 $rc(G)$, is the smallest number of colors that are…
An edge-colored graph $G$ 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…
An edge-colored graph $G$, where adjacent edges may be colored the same, is rainbow connected if any two vertices of $G$ are connected by a path whose edges have distinct colors. The rainbow connection number $rc(G)$ of a connected graph…
A path in an edge-colored graph, where adjacent edges may be colored the same, is a rainbow path if no two edges of it are colored the same. A nontrivial connected graph $G$ is rainbow connected if there is a rainbow path connecting any two…
An edge-colored graph $G$, where adjacent edges may be colored the same, is rainbow connected if any two vertices of $G$ are connected by a path whose edges have distinct colors. The rainbow connection number $rc(G)$ of a connected graph…
An edge-colored graph $G$ 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…
A path in an edge-colored graph $G$, where adjacent edges may be colored the same, is called a rainbow path if no two edges of it are colored the same. A nontrivial connected graph $G$ is rainbow connected if for any two vertices of $G$…
An edge-colored graph $G$ is {\em rainbow connected} if any two vertices are connected by a path whose edges have distinct colors. The {\em rainbow connection} of a connected graph $G$, denoted $rc(G)$, is the smallest number of colors that…
An edge-colored graph $G$ 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 $rc(G)$, is the smallest number of colors that are…
An edge colored graph $G$ is rainbow edge connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection of a connected graph $G$, denoted by $rc(G)$, is the smallest number of colors that are…
A graph is said to be \emph{total-colored} if all the edges and the vertices of the graph are colored. A path $P$ in a total-colored graph $G$ is called a \emph{total-proper path} if $(i)$ any two adjacent edges of $P$ are assigned distinct…
For a graph $G$, we define $\sigma_2(G)=min \{d(u)+d(v)| u,v\in V(G), uv\not\in E(G)\}$, or simply denoted by $\sigma_2$. A edge-colored graph is rainbow edge-connected if any two vertices are connected by a path whose edges have distinct…
The rainbow connection number, $rc(G)$, of a connected graph $G$ is the minimum number of colors needed to color its edges so that every pair of vertices is connected by at least one path in which no two edges are colored the same. We show…
An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connectivity of a connected graph G, denoted rc(G), is the smallest number of colors that are needed in…
An edge-colored graph $G$ 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…
An edge-colored graph $G$ is \emph{conflict-free connected} if, between each pair of distinct vertices, there exists a path containing a color used on exactly one of its edges. The \emph{conflict-free connection number} of a connected graph…