A polynomial algorithm for the parity path problem on perfectly orientable graphs Original Research Article

The parity path problem is to test if a graph contains an even (odd) chordless path between two prescribed vertices. A graph is called perfectly orientable if there exists an orientation of its edges such that the resulting digraph has no obstructions: an obstruction is a chordless path (a,b,c,d) having →ab and ←cd. We present a polynomial algorithm for the parity path problem on perfectly orientable graphs.