Hamiltonian factorization of a graph is a 2-factorization of the graph into Hamiltonian cycles. In this thesis we focus on finding Hamiltonian factorization or decomposition of graphs K_(2n+1), K_(n,n), K_2n- 〖nK〗_2 and finding 1-factorization of graphs K_2n and K_(n,n).
On start some general definitions and properties of a graph are needed to further understand the work. Among these are Hamiltonian paths, matchings and factors. In subsection on Matchings we prove Tutte’s theorem, in subsection of factors and factorization we define when the graph is 1-factorable or 2-factorable. In section three we present finding factorization on the example of children’s dances, as they were presented by Édouard Lucas. We illustrate these results with simple examples. For some examples we create a program code that solves the problem of factorization for concrete n.
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