GATE | GATE CS 2008 | Question 23

Which of the following statements is true for every planar graph on n vertices?
(A) The graph is connected
(B) The graph is Eulerian
(C) The graph has a vertex-cover of size at most 3n/4
(D) The graph has an independent set of size at least n/3


Answer: (C)

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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