Question 2 - Graph Theory

Let G be a simple, undirected, and connected graph with n vertices. Consider the following statements:

A. If (u, v) is a bridge in G, then at least one of the vertices u or v is a cut vertex.

B. The maximum number of bridges that G can have is n-1.

C. If G is a tree with more than 2 vertices and with f leaves, then the minimum number of edges that need to be added so that there are no bridges is ⌈f/2⌉.

Select the alternative that identifies the incorrect statements:

a) A and B

b) B and C

c) Only A

d) Only C

e) None of the above

Original Idea by Sergio Sanchez

Comentarios

  1. Joao Meidanis26 de agosto de 2024, 18:28

    Very nice question, but very difficult. How do we know that ceil(f/2) is the minimum in statement (C)?

    ResponderEliminar

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