Bound on the number of high-degree vertices in 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 $k$. High-degree vertex conjecture. For every positive integer $k$, there exists an integer $D=D(k)$ such that every $k$-crossing-critical graph contains at most $k$ vertices whose degree is larger than $D$. The construction in the source produces linearly many vertices of arbitrarily large degree in relation to $k$, motivating this conjecture as a proposed best-possible bound; its resolution is not given in the source.