On braid groups and right-angled Artin groups
A \textit{right-angled Artin group} is a group with a presentation whose only relators are commutators between generators. A. Abrams and R. Ghrist conjectured in [\textit{A. Abrams}, Geom. Dedicata 92, 185--194 (2002; Zbl 1049.20023)] and [\textit{R. Ghrist}, AMS/IP Stud. Adv. Math. 24, 29--40 (2001; Zbl 1010.55012)] that braid groups of planar graphs are right-angled Artin groups. The authors prove that contractible graphs whose nodes (vertices of degree \(\geq 3\)) all lie in an interval (copy of \([0,1]\)) have right-angled braid groups.
scientific article; zbMATH DE number 6358005