From Erdos-Renyi graphs to Linial-Meshulam complexes via the multineighbor construction

Autor:	Babson, Eric, Spaliński, Jan
Rok vydání:	2023
Předmět:	Mathematics - Combinatorics 05C80 (Primary) 62R99 (Secondary)
Druh dokumentu:	Working Paper
Popis:	The $m$-neighbor complex of a graph is the simplicial complex in which faces are sets of vertices with at least $m$ common neighbors. We consider these complexes for Erdos-Renyi random graphs and find that for certain explicit families of parameters the resulting complexes are with high probability $(t-1)$-dimensional with all $(t-2)$-faces and each $(t-1)$-face present with a fixed probability. Unlike the Linial-Meshulam measure on the same complexes there can be correlations between pairs of $(t-1)$-faces but we conjecture that the two measures converge in total variation for certain parameter sequences. Comment: 29 pages, 20 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2309.05149 Zobrazit plný text záznamu View this record from Arxiv