Probability

Graph Theory

Graph Theory - Eulerian Paths

         

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.

True or false, if GG is a connected graph with at least two nodes, then an Eulerian path in G G must visit every node.

Two graphs G G and G G' each have at least one Eulerian circuit. Let G G'' be a graph derived by combining both G G and G G' with a single edge between some node in G G to some node in G G' . Does G G'' have 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.

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