A tight bound on the length of odd cycles in the incompatibility graph of a non-C1P matrix

作者：Malekesmaeili Mehrnoush; Chauve Cedric; Stephen Tamon^*

来源：Information Processing Letters, 2012, 112(20): 799-803.

DOI：10.1016/j.ipl.2012.07.004

• Graph algorithms
• Consecutive Ones Property
• Tucker patterns
• Certifying algorithm
• Incompatibility graph

A binary matrix has the Consecutive Ones Property (C1P) if it is possible to order the columns so that all Is are consecutive in every row. In [McConnell, SODA 2004, pp. 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.

• 出版日期2012-10-31