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The Bend Number of Cocomparability Graphs

Authors Todor Antić , Vit Jelínek , Martin Pergel , Felix Schröder , Peter Stumpf , Pavel Valtr

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graphs and surfaces
Keywords
  • Intersection Graphs
  • Bend Number
  • Piecewise Linear Functions
  • Graph Class Hierarchy
  • Cocomparability Graphs
  • Permutation Graphs
  • Poset Dimension

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Abstract

We introduce a new complexity measure for cocomparability graphs of posets or in other words, intersection graphs of piecewise linear functions, the bend number. We prove that cocomparability graphs of bounded bend number are not too plentiful and give two hierarchies of classes of cocomparability graphs, depending on whether the piecewise linear functions are restricted to slopes of ±1 (diagonal case) or not (general case). These hierarchies give a gradation between permutation graphs and cocomparability graphs.

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Todor Antić, Vit Jelínek, Martin Pergel, Felix Schröder, Peter Stumpf, and Pavel Valtr. The Bend Number of Cocomparability Graphs. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 10:1-10:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.GD.2025.10

Author Details

Todor Antić
  • Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Vit Jelínek
  • Computer Science Institute, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Martin Pergel
  • Department of Software and Computer Science Education, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Felix Schröder
  • Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Peter Stumpf
  • Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
  • Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, Czech Republic
Pavel Valtr
  • Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic

Funding

  • Antić, Todor: supported by grant no. 23-04949X of the Czech Science Foundation (GAČR) and by SVV–2023–260699.
  • Jelínek, Vit: supported by grant no. 23-04949X of the Czech Science Foundation (GAČR).
  • Schröder, Felix: supported by grant no. 23-04949X of the Czech Science Foundation (GAČR).
  • Stumpf, Peter: supported by grant no. 23-04949X of the Czech Science Foundation (GAČR).
  • Valtr, Pavel: supported by grant no. 23-04949X of the Czech Science Foundation (GAČR).

Acknowledgements

We would like to thank Ida Kantor, Jelena Glišić and Maria Saumell for helpful discussions about the problems considered in this paper. We would also like to thank anonymous reviewers for their comments and suggestions, which helped improve the quality of this work.

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