On a conjecture of Godsil concerning controllable random graphs
Optimization and Control
2016-06-14 v2 Probability
Abstract
It is conjectured by Godsil that the relative number of controllable graphs compared to the total number of simple graphs on n vertices approaches one as n tends to infinity. We prove that this conjecture is true. More generally, our methods show that the linear system formed from the pair (W, b) is controllable for a large class of Wigner random matrices W and deterministic vectors b. The proof relies on recent advances in Littlewood-Offord theory developed by Rudelson and Vershynin.
Cite
@article{arxiv.1511.05080,
title = {On a conjecture of Godsil concerning controllable random graphs},
author = {Sean O'Rourke and Behrouz Touri},
journal= {arXiv preprint arXiv:1511.05080},
year = {2016}
}
Comments
32 pages; minor update