MATH HINT
Does our graph contain a Euler Path? A graph is said to be containing an Euler path if it can be traced in 1 sweep without lifting the pencil from the paper and without tracing the same edge more than once. Vertices may be passed through more than once. The starting and ending points need not be the same.
How can we tell if a graph contains a Euler Path mathematically?
A graph with all vertices being even contains a Euler circuit
A graph with 2 odd vertices and some even vertices contains a Euler path
A graph with more than 2 odd vertices does not contain any Euler path or circuit
How can we tell if a graph contains a Euler Path mathematically?
A graph with all vertices being even contains a Euler circuit
A graph with 2 odd vertices and some even vertices contains a Euler path
A graph with more than 2 odd vertices does not contain any Euler path or circuit