Rainbow Vertex-Connection Number of 3-Connected Graph
نویسندگان
چکیده
A path in an edge colored graph is said to be a rainbow path if every edge in this colored with the same color. A vertex-colored graph G is rainbow vertex-connected if any pair of vertices in G are connected by a path whose internal vertices have distinct colors. The rainbow vertexconnection number of G denoted by rvc(G), is the smallest number of colors that are needed in order to make G rainbow vertexconnected. In this paper, we proved that rvc(G) ≤ 3(n+2) 5 for 3-connected graph except to s+ t ≥ 3. Mathematics Subject Classification: 05C15, 05C40
منابع مشابه
On Rainbow Connection Number and Connectivity
Rainbow connection number, rc(G), of a connected graph G is the minimum number of colours needed to colour its edges, so that every pair of vertices is connected by at least one path in which no two edges are coloured the same. In this paper we investigate the relationship of rainbow connection number with vertex and edge connectivity. It is already known that for a connected graph with minimum...
متن کاملThe rainbow connection of a graph is (at most) reciprocal to its minimum degree
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 needed in order to make G rainbow edgeconnected. We prove that if G has n vertices and minimum degree δ then rc(G) < 20n/δ. This solves open problems from [5] and...
متن کاملVertex rainbow colorings of graphs
In a properly vertex-colored graphG, a path P is a rainbow path if no two vertices of P have the same color, except possibly the two end-vertices of P . If every two vertices of G are connected by a rainbow path, then G is vertex rainbow-connected. A proper vertex coloring of a connected graph G that results in a vertex rainbow-connected graph is a vertex rainbow coloring ofG. The minimum numbe...
متن کاملRainbow connections for planar graphs and line graphs
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 are needed in order to make G rainbow connected. It was proved that computing rc(G) is an NP-Hard problem, as well as that even deciding whether a graph has rc(G) =...
متن کاملComputing Minimum Rainbow and Strong Rainbow Colorings of Block Graphs
A path in an edge-colored graph G is rainbow if no two edges of it are colored the same. The graph G is rainbow-connected if there is a rainbow path between every pair of vertices. If there is a rainbow shortest path between every pair of vertices, the graph G is strongly rainbow-connected. The minimum number of colors needed to make G rainbow-connected is known as the rainbow connection number...
متن کامل