Name
Title | ||
|---|---|---|
A tight bound on the length of odd cycles in the incompatibility graph of a non-C1P matrix |
Abstract | ||
|---|---|---|
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, 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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.ipl.2012.07.004 | Information Processing Letters |
Keywords | DocType | Volume |
binary matrix,non-c1p matrix,k column,odd cycle,smallest odd cycle,tucker pattern,incompatibility graph,data structure | Journal | 112 |
Issue | ISSN | Citations |
20 | 0020-0190 | 1 |
PageRank | References | Authors |
0.39 | 4 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Mehrnoush Malekesmaeili | 1 | 1 | 0.39 |
| cedric chauve | 2 | 429 | 41.81 |
| Tamon Stephen | 3 | 121 | 16.03 |