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
C) TRUE:
D) FALSE:
Quiz of this Question
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