This paper deals with Hável and Erdös conjecture that asserts that all bipartite graph formed with the middle levels of n-dimensional cube is Hamiltonian, when n is odd. This means that at least one Hamiltonian cycle should be found in the graph. We use a circular representation of the vertices of n-dimensional cube which makes it possible to introduce two group actions in order to reduce the problem to find out a Hamiltonian path in multi-level quotient graphs. We report on a hybrid genetic algorithm for the Hável and Erdös conjecture problem. We present interesting results which show that this GA approach gives optimal solutions in multi-level quotient graph. We use bitstring representation, an evolutionary fitness function, restricted edge crossover operator, intelligent mutation, seeding and adaptative mutation rate. Three Hamiltonian paths are constructed with this method.
