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




Quiz of this Question

My Personal Notes arrow_drop_up

Article Tags :


Please write to us at to report any issue with the above content.