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We mainly focus in this paper the maximum number of cycles in the union of two trees. In order to prove non-trivial bounds we also need some upper bounds on the number of Hamiltonian cycles in 3- and 4-regular graphs.
Bibtex entry:
| AUTHOR | = | {Kir{\'a}ly, Zolt{\'a}n}, |
| TITLE | = | {Maximum Number of Cycles and Hamiltonian Cycles in Sparse Graphs}, |
| NOTE | = | {{\tt egres.elte.hu}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2009}, |
| NUMBER | = | {TR-2009-03} |