All pairs suffice
Combinatorics
2014-12-09 v1
Abstract
A P-set of a symmetric matrix is a set of indices such that the nullity of the matrix obtained from by removing rows and columns indexed by is more than that of . It is known that each subset of a P-set is a P-set. It is also known that a set of indices such that each singleton subset is a P-set need not be a P-set. This note shows that if all pairs of vertices of a set with at least two elements are P-sets, then the set is a P-set.
Keywords
Cite
@article{arxiv.1412.2292,
title = {All pairs suffice},
author = {Curtis G. Nelson and Bryan L. Shader},
journal= {arXiv preprint arXiv:1412.2292},
year = {2014}
}