Note on a min‐max conjecture of Woodall

In 1978 Woodall 6 ] conjectured the following: in a planar digraph the size of a shortest cycle is equal to the maximum cardinality of a collection of disjoint tranversals of cycles. We prove that this conjecture is true when the digraph is series‐parallel. In fact, we prove a stronger weighted version that gives the latter result as a corollary. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 36–41, 2001