I present an algorithm that can solve Hamiltonian cycle problem relatively fast for many graphs. Algorithm tests if a Hamiltonian cycle exists in directed graph, if it is exists algorithm can show found Hamiltonian cycle. If you want to test an undirected graph, such a graph should be converted to the form of directed graph.

In order to find Hamiltonian cycle, algorithm should find edges that creates a Hamiltonian cycle. Algorithm uses recursive depth-first search. Algorithm rests on analysis of original graph and opposite graph to it. Algorithm prefers ''to think over'' which paths should be checked than check many wrong paths. Algorithm can:

• remove unnecessary edges from graph
• test when Hamiltonian cycle can't exist in graph
• choose most optimal path

Algorithm description:

http://arxiv.org/pdf/1405.6347.pdf