On the topological Kalai-Meshulam conjecture

Autor:	Engstrom, Alexander
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics Mathematics - Algebraic Topology Mathematics - Geometric Topology
Druh dokumentu:	Working Paper
Popis:	Chudnovsky, Scott, Seymour and Spirkl recently proved a conjecture by Kalai and Meshulam stating that the reduced Euler characteristic of the independence complex of a graph without induced cycles of length divisible by three is in {-1,0,1}. Gauthier had earlier proved that assuming no cycles of those lengths, induced or not. Kalai and Meshulam also stated a stronger topological conjecture, that the total betti numbers are in {0,1}. Towards that we prove an even stronger statement in the same setting as Gauthier: The independence complexes are either contractible or homotopy equivalent to spheres. We conjecture that it also holds in the general setting. Comment: 8 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2009.11077 Zobrazit plný text záznamu View this record from Arxiv