Displaying similar documents to “On the Rainbow Vertex-Connection”

Rainbow Vertex-Connection and Forbidden Subgraphs

Wenjing Li, Xueliang Li, Jingshu Zhang (2018)

Discussiones Mathematicae Graph Theory

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A path in a vertex-colored graph is called vertex-rainbow if its internal vertices have pairwise distinct colors. A vertex-colored graph G is rainbow vertex-connected if for any two distinct vertices of G, there is a vertex-rainbow path connecting them. For a connected graph G, the rainbow vertex-connection number of G, denoted by rvc(G), is defined as the minimum number of colors that are required to make G rainbow vertex-connected. In this paper, we find all the families ℱ of connected...

On rainbow connection.

Caro, Yair, Lev, Arie, Roditty, Yehuda, Tuza, Zsolt, Yuster, Raphael (2008)

The Electronic Journal of Combinatorics [electronic only]

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The Vertex-Rainbow Index of A Graph

Yaping Mao (2016)

Discussiones Mathematicae Graph Theory

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The k-rainbow index rxk(G) of a connected graph G was introduced by Chartrand, Okamoto and Zhang in 2010. As a natural counterpart of the k-rainbow index, we introduce the concept of k-vertex-rainbow index rvxk(G) in this paper. In this paper, sharp upper and lower bounds of rvxk(G) are given for a connected graph G of order n, that is, 0 ≤ rvxk(G) ≤ n − 2. We obtain Nordhaus-Gaddum results for 3-vertex-rainbow index of a graph G of order n, and show that rvx3(G) + rvx3(Ḡ) = 4 for n...

Vertex rainbow colorings of graphs

Futaba Fujie-Okamoto, Kyle Kolasinski, Jianwei Lin, Ping Zhang (2012)

Discussiones Mathematicae Graph Theory

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In a properly vertex-colored graph G, 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 of G. The minimum number of colors needed in a vertex rainbow coloring of G is the vertex rainbow connection number...