Khovanov-Rozansky homology and Directed Cycles

2015/08/28 by Hao Wu, Wu, Hao
Computer Science · Mathematics · #05C20 #05C38 (Primary) #13P25 (Secondary) #14N10 #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1508.07337

openalex publication_date 2015/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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