Crossing-critical graphs with large maximum degree

A conjecture of Richter and Salazar about graphs that are critical for a fixed crossing number k is that they have bounded bandwidth. A weaker well-known conjecture of Richter is that their maximum degree is bounded in terms of k. In this note we disprove these conjectures for every k ⩾ 171 , by providing examples of k-crossing-critical graphs with arbitrarily large maximum degree.