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Rainbow Vertex-Connection and Forbidden Subgraphs

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Li W., Li X., Zhang J.

Discussiones Mathematicae Graph Theory

2017

tom 38

nr 1

143-154

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 graphs with |ℱ| ∈ {1, 2}, for which there is a constant kℱ such that, for every connected ℱ-free graph G, rvc(G) ≤ diam(G) + kℱ, where diam(G) is the diameter of G.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Li W.

1 Li X.

1 Zhang J.

1 2018

Wyniki wyszukiwania

Rainbow Vertex-Connection and Forbidden Subgraphs