Ghrist's conjecture on planar graph braid groups

Let $\Gamma$ be a planar graph, and let $B_n\Gamma$ and $P B_n\Gamma$ denote its $n$-strand braid group and pure braid group, respectively. A group is right-angled Artin if it admits a presentation whose defining relators are commutators of pairs of generators. Ghrist's conjecture. The (pure) braid group of any planar graph is a right-angled Artin group. The conjecture is significant because it predicts a particularly tractable algebraic structure for braid groups arising from planar graphs. The paper gives counterexamples, so the conjecture is refuted.