  In this note we show that any embedded graph has a checkerboard colourable
twisted dual and any Eulerian embedded graph has a checkerboard colourable
partial Petrial, answering questions posed by Ellis-Monaghan and Moffatt. The
proofs are based on orientations of their medial graphs and orientations of
boundary components of their corresponding ribbon graphs. The arrow
presentations of ribbon graphs are also used. We also obtain two related
results.
