A graph with two vertices of odd degree and three vertices of even degree will always contain at least one Euler Path. This statement is
A) always true.
B) always false.
C) true only if the graph is connected.
D) false only if the graph is connected.
E) None of the above.

Question

Quizplus · Accepted Answer

A graph will contain an Euler Path if and only if it has exactly 0 or 2 vertices of odd degree and if it is connected. Since the graph mentioned has exactly two vertices of odd degree, it satisfies one condition for having an Euler Path. However, it must also be connected to ensure the existence of such a path.

A Graph with Two Vertices of Odd Degree and Three