Hello,
How would I go about efficiently finding if an even cycle exists in a directed graph? I know for odd cycles we can simply run a bipartition algorithm and if it doesn't work we know there exists an odd cycle. But how do I do that for even cycles?
Easy and general answer to many questions: Search on a popular search engine (for example google).
Third search result: link
Now, you can go ahead and look over the comments. You also have explanations of why some solutions are wrong.
nvm
Because an even cycle can exist even though the graph is not bipartite