On the queue-number of graphs with bounded tree-width

Veit Wiechert¹

¹Technische Universität Berlin

The electronic journal of combinatorics, Tome 24 (2017) no. 1

Résumé

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 $3$.

Détail

DOI : 10.37236/6429

Classification : 05C05, 05C12
Mots-clés : graph layouts, queue layouts, tree-width