Given a directed graph, we want to decide whether it contains a directed cycle of even length. This 1997 paper by YUSTER and ZWICK states that the problem is not known to be in $P$ nor is it known to be $NP$-complete.

Is there any recent result that resolves the complexity of the even cycle problem in directed graphs?


1 Answer 1


Yes, a polynomial time algorithm was first given in:

Neil Robertson, P. D. Seymour, Robin Thomas. "Permanents, Pfaffian orientations, and even directed circuits." Annals of Mathematics 150.3 (1999): 929-975. arXiv

edit: Actually, according to the acknowledgements section of the above paper, the result was first obtained by McCuaig who later published it as:

William McCuaig. "Pólya's Permanent Problem." Electr. J. Comb. 11(1) (2004) http://www.combinatorics.org/ojs/index.php/eljc/article/view/v11i1r79

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    $\begingroup$ Thanks for the quick answer. Nice topological characterization. $\endgroup$ Commented Nov 7, 2013 at 14:33

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