A Hamiltonian game on Kn,n Original Research Article

Let Kn,n be the complete bipartite graph of order 2n. Two players, maker and breaker, alternately take previously untaken edges of Kn,n, one edge per move, with the breaker going first. The game ends when all edges of Kn,n have been taken. Then the edges taken by the maker induce a graph G. The maker wants G to have as many edge disjoint Hamilton cycles as possible. We prove that the maker can achieve 137 n edge-disjoint Hamilton cycles for large n.