2012/07/20 by Eric Babson, Babson, Eric · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Random Matrices and Applications #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1207.5028
openalex publication_date 2012/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Clique complexes of Erdős-Rényi random graphs with edge probability between n^-1\over 3 and n^-1\over 2 are shown to be aas not simply connected. This entails showing that a connected two dimensional simplicial complex for which every subcomplex has fewer than three times as many edges as vertices must have the homotopy type of a wedge of circles, two spheres and real projective planes. Note that n^-1\over 3 is a threshold for simple connectivity and n^-1\over 2 is one for vanishing first \F2 homology.