# On the Queue-Number of Graphs with Bounded Tree-Width

Keywords:
Graph layouts, Queue layouts, Tree-width,

### Abstract

A*queue layout*of a graph consists of a linear order on the vertices and an assignment of the edges to

*queues*, such that no two edges in a single queue are nested. The minimum number of queues needed in a queue layout of a graph is called its

*queue-number*.

We show that for each $k\geq0$, graphs with tree-width at most $k$ have queue-number at most $2^k-1$. This improves upon double exponential upper bounds due to Dujmović et al. and Giacomo et al. As a consequence we obtain that these graphs have track-number at most $2^{O(k^2)}$.

We complement these results by a construction of $k$-trees that have queue-number at least $k+1$. Already in the case $k=2$ this is an improvement to existing results and solves a problem of Rengarajan and Veni Madhavan, namely, that the maximal queue-number of $2$-trees is equal to $3$.