Richter and Salazar's bounded-bandwidth conjecture for crossing-critical graphs

A graph is $k$-crossing-critical if its crossing number is at least $k$, but every proper subgraph has crossing number smaller than $k$. Richter and Salazar's conjecture. For every positive integer $k$, there exists an integer $B(k)$ such that every $k$-crossing-critical graph has bandwidth at most $B(k)$. The source states that this conjecture, proposed as an open problem by Carsten Thomassen in the 1990s and formulated by Richter and Salazar, is disproved in the paper for every $k\geq 171$ by examples with arbitrarily large maximum degree; the abstract presents the two conjectures as disproved together.