   Chapter 10.1, Problem 31ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Show that none of graphs in 31-33 has a Hamiltonian circuit. To determine

To prove:

Show that the graph does not have a Hamiltonian circuit. Explanation

Given information:

Proof:

Given a graph G, from the subgraph H’ consisting all vertices of degree 2 and their incident edges.

If H contains a vertex with degree > 2, then G has no Hamiltonian circuit.

If H has a vertex of degree > 2, then so does H, which is impossible since H is a circuit.

If H contains a circuit, but V(H)V(G), then G has no Hamiltonian circuit

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