On the Recognition of Outerplanar Graphs with Queue Number 1

Michael A. Bekos; Thomas Depian; Stefan Felsner; Michael Kaufmann; Philipp Kindermann; Fabrizio Montecchiani; Maria Eleni Pavlidi; Alexandra Weinberger; Alexander Wolff; Johannes Zink

arXiv · 2607.24297

On the Recognition of Outerplanar Graphs with Queue Number 1

Michael A. Bekos·Thomas Depian·Stefan Felsner·Michael Kaufmann·Philipp Kindermann·Fabrizio Montecchiani·Maria Eleni Pavlidi·Alexandra Weinberger·Alexander Wolff·Johannes Zink

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Abstract

A linear layout of a graph is defined as a total order of the vertices and a partition of the edges to pages. In a stack (queue) layout, no two edges on the same page may cross (nest). The stack (queue) number of a graph is the minimum number of pages required in a stack (queue) layout. This paper focuses on characterizing and recognizing graphs that have both stack number 1 and queue number 1. It is known that the graphs with stack number 1 are exactly the outerplanar graphs. We show that (i) deciding whether a given outerplanar graph has queue number 1 is NP-hard; (ii) deciding whether a given maximal outerplanar graph has queue number 1 can be done in linear time. Moreover, we investigate the interplay between outerpaths with queue number 1 and their maximum vertex degree.

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Michael A. Bekos, Thomas Depian, Stefan Felsner, Michael Kaufmann, Philipp Kindermann, Fabrizio Montecchiani, Maria Eleni Pavlidi, Alexandra Weinberger, Alexander Wolff, Johannes Zink. 2026-07-27. On the Recognition of Outerplanar Graphs with Queue Number 1. https://arxiv.org/abs/2607.24297

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