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GATE | GATE CS 2008 | Question 23

Last Updated : 15 Feb, 2018
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Which of the following statements is true for every planar graph on n vertices?
 

(A)

The graph has a vertex-cover of size at most 3n/4
 

(B)

The graph is Eulerian
 

(C)

The graph is connected
 

(D)

The graph has an independent set of size at least n/3
 


Answer: (A)

Explanation:

A planar graph is a graph which can drawn on a plan without any pair of edges crossing each other. 

A) FALSE: A disconnected graph can be planar as it can be drawn on a plane without crossing edges. 

B) FALSE: An Eulerian Graph may or may not be planar. An undirected graph is eulerian if all vertices have even degree.

For example, the following graph is Eulerian, but not planar 

 

\"Complete_graph_K5.svg\"

C) TRUE: 

D) FALSE: 

 


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