2016/04/18 by Shuchita Goyal, Goyal, Shuchita, Rekha Santhanam +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Retinoids in leukemia and cellular processes #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1604.05135
openalex publication_date 2016/04/18 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28
In this article, we give conditions on a graph under which the Lovász' original bound of the graph can be improved by increasing the topological connectivity of its neighbourhood complex. We also work out conditions under which computing the topological connectivity of hom complex of a pair of graphs can be simplified. In particular, hom complex as a covariant functor acting on a double mapping cylinder of graphs is a homotopy pushout of hom complex functor applied to its subgraphs. We give applications of this result where the computation of hom complexes is simplified. Finally, we explain why double mapping cylinder of graphs does not give a satisfactory definition of homotopy pushout in the category of graphs.