Mixed-colour closed walk criterion
= Mixed-colour closed walk criterion
A <directed graph> with black and white <edges> has a <closed walk> containing both colours exactly when some <strongly connected component> has internal <edges> of both colours. Join the two chosen <edges> with <graph paths> inside the <strongly connected component>. A corresponding claim for a <simple cycle> is false: differently coloured <graph cycles> can meet at a single <vertex>.