An upper bound theorem for a class of flag weak pseudomanifolds

2013/03/22 by Michał Adamaszek, Michal Adamaszek, Adamaszek, Michal
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Topological and Geometric Data Analysis #math.CO

paper · pdf · doi:10.48550/arxiv.1303.5603

arxiv created 2013/03/22 · openalex publication_date 2013/03/22 · arxiv updated 2013/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

If K is an odd-dimensional flag closed manifold, flag generalized homology sphere or a more general flag weak pseudomanifold with sufficiently many vertices, then the maximal number of edges in K is achieved by the balanced join of cycles. The proof relies on stability results from extremal graph theory. In the case of manifolds we also offer an alternative (very) short proof utilizing the non-embeddability theorem of Flores. The main theorem can also be interpreted without the topological contents as a graph-theoretic extremal result about a class of graphs such that 1) every maximal clique in the graph has size d+1 and 2) every clique of size d belongs to exactly two maximal cliques.

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• A generalized lower bound theorem for balanced manifolds