(1) If the degree of the vertices are 2,2,3,4, can G have an Euler circuit? Recall that an
Euler circuit of a graph is a circuit where each vertex of the graph appears at least once in
the circuit.
(2) Draw a graph G with 4 vertices that has a Hamiltonian circuit but that does not
have an Euler circuit. Recall a Hamiltonian circuit in a graph is a circuit where each
vertex except the first and last ones (which have to be the same) appears exactly once.
(3) Write down a graph with exactly 3 vertices that has an Euler circuit but not Hamil-
tonian circuits.