Khovanov-Rozansky homology and Directed Cycles
arXiv:1508.07337
Abstract
We determine the cycle packing number of a directed graph using elementary projective algebraic geometry. Our idea is rooted in the Khovanov-Rozansky theory. In fact, using the Khovanov-Rozansky homology of a graph, we also obtain algebraic methods of detecting directed and undirected cycles containing a particular vertex or edge.
28 pages, no figures. Version 3: added a computation of the cycle packing number; Version 4: minor updates and corrections