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Description:
The best worst case guarantee algorithm to see if a graph has a Hamiltonian cycle, a closed tour visiting every vertex exactly once, for a long time was based on dynamic programming over all the vertex subsets of the graph. In this talk we will show some algebraic techniques that can be used to see if a graph has a Hamiltonian cycle much faster. These techniques utilize sums over determinants of matrices. In particular we will show how you can find out if an undirected graph has a Hamiltonian cycle much faster, but we will also talk about some partial results for the directed case and modular counting.