Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A tight bound on the length of odd cycles in the incompatibility graph
  of a non-C1P matrix   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.

14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat