11 th International Symposium on Parameterized and Exact Computation

The best worst case guarantee algorithm to see if a graph has a Hamiltonian cycle, a closed tourvisiting every vertex exactly once, for a long time was based on dynamic programming over allthe vertex subsets of the graph. In this talk we will show some algebraic techniques that can beused to see if a graph has a Hamiltonian cycle much faster. These techniques utilize sums overdeterminants of matrices.In particular we will show how you can find out if an undirected graph has a Hamiltoniancycle much faster, but we will also talk about some partial results for the directed case andmodular counting. 1998 ACM Subject Classification G.2.2 Graph Algorithms, I.1.2 Analysis of Algorithms