In 2003, Prowse and Woodall proved that for graphs $C_n^k$ which are powers of cycles, $$\chi_\ell(C_n^k) = \chi(C_n^k).$$ They conjectured that this equality holds for the broader class of graphs known as circular-arc graphs. I am wondering whether this conjecture has been resolved one way or another.
Searching for "circular arc graph" within the papers referencing Prowse and Woodall, and checking Math Stack Exchange and Overflow for previous questions about circular arc graphs, has so far turned up nothing.
