Khovanov-Rozansky homology and Directed Cycles
Combinatorics
2017-03-30 v4 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.1508.07337,
title = {Khovanov-Rozansky homology and Directed Cycles},
author = {Hao Wu},
journal= {arXiv preprint arXiv:1508.07337},
year = {2017}
}
Comments
28 pages, no figures. Version 3: added a computation of the cycle packing number; Version 4: minor updates and corrections