Bounded-Degree Graphs have Arbitrarily Large Queue-Number
Abstract
Description
It is proved that there exist graphs of bounded degree with arbitrarily large queue-number. In particular, for all $Δ\geq3$ and for all sufficiently large $n$, there is a simple $Δ$-regular $n$-vertex graph with queue-number at least $c\sqrtΔn^{1/2-1/Δ}$ for some absolute constant $c$.