Maguy Trefois, Jean-Charles Delvenne
Published 2012-04-06, updated 2014-06-13Version 2
The minimum rank of a graph is the minimum possible rank of a real matrix whose zero-nonzero pattern is described by the graph. The current algorithms can compute efficiently the minimum rank of undirected trees. This paper provides an algorithm to compute in polynomial time the minimum rank of directed trees allowing loops.
Comments: This paper has been withdrawn due to a crucial error in Lemma 5.2. A correct and more complete version is available here: arXiv:1405.6222. In particular, in this new version we identify a class of directed trees allowing loops whose minimum rank is computable in linear time. An efficient algorithm for the minimum rank of any directed tree allowing loops is still needed
Minimum ranks of sign patterns via sign vectors and duality
Graph classes for critical ideals, minimum rank and zero forcing number
Testing isomorphism of circulant objects in polynomial time
![QR code for arXiv:1204.1444 [math.CO]](http://oss.arxitics.com/images/favicon.svg)