Discrete Mathematics
# Graph Theory

What must be true of a path that is an Eulerian path?

True or false, if a graph has an Eulerian path then it has an Eulerian circuit.

Suppose a connected graph has 15 nodes. Given that is has an Eulerian circuit, what is the minimum number of distinct Eulerian circuits which it must have?

NOTE: A circuit uses an ordered list of nodes, so a circuit with nodes 1-2-3 is considered distinct from a circuit with nodes 2-3-1.