  A binary matrix has the consecutive ones property (C1P) if it is possible to
order the columns so that all 1s are consecutive in every row. In [McConnell,
SODA 2004 768-777] the notion of incompatibility graph of a binary matrix was
introduced and it was shown that odd cycles of this graph provide a certificate
that a matrix does not have the consecutive ones property. A bound of (k+2) was
claimed for the smallest odd cycle of a non-C1P matrix with k columns. In this
note we show that this result can be obtained simply and directly via Tucker
patterns, and that the correct bound is (k+2) when k is even, but (k+3) when k
is odd.
