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
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