English

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