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Simultaneous Representation of Interval Graphs in the Sunflower Case

Authors Ignaz Rutter , Peter Stumpf

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Author Details

Ignaz Rutter
  • Faculty of Computer Science and Mathematics, University of Passau, Germany
Peter Stumpf
  • Faculty of Computer Science and Mathematics, University of Passau, Germany

Funding

This work was funded by grant RU 1903/3-1 of the German Research Foundation (DFG).

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Ignaz Rutter and Peter Stumpf. Simultaneous Representation of Interval Graphs in the Sunflower Case. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 90:1-90:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.90

Abstract

A simultaneous representation of (vertex-labeled) graphs G_1,… ,G_k consists of a (geometric) intersection representation R_i for each graph G_i such that each vertex v is represented by the same geometric object in each R_i for which G_i contains v. While Jampani and Lubiw showed that the existence of simultaneous interval representations for k = 2 can be tested efficiently (2010), testing it for graphs where k is part of the input is NP-complete (Bok and Jedličková, 2018). An important special case of simultaneous representations is the sunflower case, where G_i ∩ G_j = (V(G_i)∩ V(G_j),E(G_i)∩ E(G_j)) is the same graph for each i ≠ j. We give an O(∑_{i=1}^k (|V(G_i)|+|E(G_i)|))-time algorithm for deciding the existence of a simultaneous interval representation for the sunflower case, even when k is part of the input. This answers an open question of Jampani and Lubiw.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Interval Graphs
  • Sunflower Case
  • Simultaneous Representation
  • Recognition
  • Geometric Intersection Graphs

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