2022/10/31 by Alexander Kamal, Kamal, Alexander, Роман Карасев +1
Chemistry · Computer Science · Physics and Astronomy · #05C12 #05C15 #05C35 #51F99 #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #History and advancements in chemistry #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2210.17090
openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the discrete versions of the systolic inequality that estimate the number of vertices of a simplicial complex from below have substantial applications to graphs, the one-dimensional simplicial complexes. Almost directly they provide good estimates for the number of vertices of a graph in terms of its chromatic number and the length of the smallest odd cycle. Combined with the graph-theoretic techniques of Berlov and Bogdanov, the systolic approach produces even better estimates.