Bounded-Degree Graphs have Arbitrarily Large Queue-Number

Abstract

It is proved that there exist graphs of bounded degree with arbitrarily large queue-number. In particular, for all $\Delta\geq3$ and for all sufficiently large $n$, there is a simple $\Delta$-regular $n$-vertex graph with queue-number at least $c\sqrt{\Delta}n^{1/2-1/\Delta}$ for some absolute constant $c$.