Rainbow Vertex-Connection and Forbidden Subgraphs

• Autorzy: Wenjing Li , Xueliang Li , Jingshu Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

vertex-rainbow path; rainbow vertex-connection; forbidden sub-graphs

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C35: Extremal problems
• 05C38: Paths and cycles
• 05C40: Connectivity

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2017
• Tom: 38
• Numer: 1
• Strony: 143-154

Daty

wydano

2018-02-01

otrzymano

2016-02-25

poprawiono

2016-10-21

zaakceptowano

2016-10-21

online

2017-12-30

Twórcy

autor

Wenjing Li

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autor

Xueliang Li

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autor

Jingshu Zhang

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Identyfikatory

DOI

10.7151/dmgt.2004