**SEMINARIO DE TEORÍA DE GRUPOS**

Vertex separators, chordality and virtually free groups

**Ponente:** Samuel Gutiérrez Corregidor (UCM)

**Fecha:** Martes, 22 de junio de 2021 - 11:30

**Lugar:** Online

**Resumen:** A graph G satisfies the bottleneck property (BP) if there exists some constant D > 0 so that given any two distinct vertices x,y of G and a vertex c such that d(x,c) = d(y,c) = 1/2 d(x,y), then every xy-path intersects the D-neighbourhood of c. A graph G is e-densely (k,m)-chordal if for every cycle p in G with length L(p) > k, there exist strict shortcuts s_1 , ... , s _r with L(s_i) < m for all i, and such that their associated shortcut vertices define an e-dense subset in (p,d_p). These definitions can be re-written in new terms given a group presentation. In the context of groups, this gives two characterizations for a group to be virtually free.