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≥1, graphs with tree-width at most k have queue-number at most 2k−1. This improves upon double exponential upper bounds due to Dujmovi\'c et al. and Giacomo et al. As a consequence we obtain that these graphs have track-number at most 2O(k2). 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.
@article{arxiv.1608.06091,
title = {On the queue-number of graphs with bounded tree-width},
author = {Veit Wiechert},
journal= {arXiv preprint arXiv:1608.06091},
year = {2016}
}