The crossing-number and braid-index inequality for special alternating links

Let $L$ be a special alternating link. Write $c(L)$ for its crossing number, $g(L)$ for its genus, and $b(L)$ for its braid index. Special alternating link inequality. One has

$$c(L)-g(L)\ge 2\bigl(b(L)-1\bigr).$$

The inequality is proposed as a link analogue of an experimentally supported bound for special alternating knots; the paper reports verification in the knot cases considered but leaves the link statement open.