In 34-37, find Hamiltonian circuits for those graphs that have them. Explain why the other graphs do not.
Find Hamiltonian circuits for those graphs that have them. Explain why the other graphs do not.
Given a graph G, from the subgraph consisting all vertices of degree 2 and their incident edges.
If G has a Hamiltonian circuit H (which we consider as a subgraph of G ), then it must contain H’ as a subgraph, since a Hamiltonian circuit must include every edge incident on a vertex of degree 2.
If contains a vertex with degree > 2, then G has no Hamiltonian circuit.
If has a vertex of degree > 2, then so does H, which is impossible since H is a circuit.
If contains a circuit, but , then G has no Hamiltonian circuit
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