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arXiv · 1511.05080

On a conjecture of Godsil concerning controllable random graphs

Sean O'Rourke·Behrouz Touri
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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.

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Sean O'Rourke, Behrouz Touri. 2015-11-16. On a conjecture of Godsil concerning controllable random graphs. https://arxiv.org/abs/1511.05080

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