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Unformatted text preview: K n . (c) [BB] Kn has n(n 21) edges, so the maximum is n 2 1 edge disjoint cycles. (d) If n = 2, there are no Hamiltonian cycles (and therefore no edge disjoint ones). 1 If n = 3, the graph is ~. 2 3 no edge disjoint Hamiltonian cycles. 1 2 Ifn ~ 4, thegmphis ~ 4 3 ~ Ifn= 5, the graph is 5~3. 4 123 and 132 are the only Hamiltonian cycles; so there are The Hamiltonian cycles are 1234, 1243, 1324, 1342, 1423 and 1432. No pair are edge disjoint. The Hamiltonian cycles are 12345, 12354, 12435, 12453,12534,12543,13245,13254,13425,13452, 13524,13542,14235,14253,14325,14352,14523, 14532,15234,15243,15324,15342,15423,15432. Since n;l = 2, we could possibly have two edge disjoint cycles and we do; for instance, 12345 and 13524. 12. [BB] The cube is indeed Hamiltonian; the labels 1, ... ,8 on the vertices exhibit a Hamiltonian cycle. LQ) : 1 8 J~ .."" ~ 4 5 13. 1 3...
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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