  In new progress on conjectures of Stein, and Addario-Berry, Havet, Linhares
Sales, Reed and Thomass\'e, we prove that every oriented graph with all in- and
out-degrees greater than 5k/8 contains an alternating path of length k. This
improves on previous results of Klimo\v{s}ov\'a and Stein, and Chen, Hou and
Zhou.
