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Documents authored by Haase, Carolina

Document
DOI: 10.4230/LIPIcs.GD.2025.13
Separability of Witness Gabriel Drawings

Authors: Carolina Haase, Philipp Kindermann, William Lenhart, and Giuseppe Liotta

Published in: LIPIcs, Volume 357, 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)

Abstract
A witness Gabriel drawing Γ is a straight-line drawing of a graph in which any two vertices of Γ are adjacent if and only if the disk having these vertices as antipodal points contains no element of a special set of points called witnesses. A witness Gabriel drawing is linearly separable if the vertices and the witnesses lie in opposite half-planes. We prove that every outerplanar graph has a linearly separable witness Gabriel drawing by introducing and studying a new type of drawing that we call a border parabola drawing. We then use border parabola drawings to characterize those triangle-free graphs that admit a linearly separable witness Gabriel drawing. We also consider witness Gabriel drawings where no witness lies in the interior of the convex hull of the vertex set, which we call convexly separable drawings. We construct witness Gabriel drawable graphs for which any witness Gabriel drawing must be convexly separable and that do not admit any linearly separable witness Gabriel drawing.
Cite as

Carolina Haase, Philipp Kindermann, William Lenhart, and Giuseppe Liotta. Separability of Witness Gabriel Drawings. In 33rd International Symposium on Graph Drawing and Network Visualization (GD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 357, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haase_et_al:LIPIcs.GD.2025.13,
  author =	{Haase, Carolina and Kindermann, Philipp and Lenhart, William and Liotta, Giuseppe},
  title =	{{Separability of Witness Gabriel Drawings}},
  booktitle =	{33rd International Symposium on Graph Drawing and Network Visualization (GD 2025)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-403-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{357},
  editor =	{Dujmovi\'{c}, Vida and Montecchiani, Fabrizio},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GD.2025.13},
  URN =		{urn:nbn:de:0030-drops-249998},
  doi =		{10.4230/LIPIcs.GD.2025.13},
  annote =	{Keywords: Proximity Drawings, Witness Gabriel Graphs, Geometric Graph Theory}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2025.9
Geometric Realizations of Dichotomous Ordinal Graphs

Authors: Patrizio Angelini, Sabine Cornelsen, Carolina Haase, Michael Hoffmann, Eleni Katsanou, Fabrizio Montecchiani, Raphael Steiner, and Antonios Symvonis

Published in: LIPIcs, Volume 332, 41st International Symposium on Computational Geometry (SoCG 2025)

Abstract
A dichotomous ordinal graph consists of an undirected graph with a partition of the edges into short and long edges. A geometric realization of a dichotomous ordinal graph G in a metric space X is a drawing of G in X in which every long edge is strictly longer than every short edge. We call a graph G pandichotomous in X if G admits a geometric realization in X for every partition of its edge set into short and long edges. We exhibit a very close relationship between the degeneracy of a graph G and its pandichotomic Euclidean or spherical dimension, that is, the smallest dimension k such that G is pandichotomous in ℝ^k or the sphere 𝒮^k, respectively. First, every d-degenerate graph is pandichotomous in ℝ^d and 𝒮^{d-1} and these bounds are tight for the sphere and for ℝ² and almost tight for ℝ^d, for d ≥ 3. Second, every n-vertex graph that is pandichotomous in ℝ^k has at most μ kn edges, for some absolute constant μ < 7.23. This shows that the pandichotomic Euclidean dimension of any graph is linearly tied to its degeneracy and in the special case k ∈ {1,2} resolves open problems posed by Alam, Kobourov, Pupyrev, and Toeniskoetter. Further, we characterize which complete bipartite graphs are pandichotomous in ℝ²: These are exactly the K_{m,n} with m ≤ 3 or m = 4 and n ≤ 6. For general bipartite graphs, we can guarantee realizations in ℝ² if the short or the long subgraph is constrained: namely if the short subgraph is outerplanar or a subgraph of a rectangular grid, or if the long subgraph forms a caterpillar.
Cite as

Patrizio Angelini, Sabine Cornelsen, Carolina Haase, Michael Hoffmann, Eleni Katsanou, Fabrizio Montecchiani, Raphael Steiner, and Antonios Symvonis. Geometric Realizations of Dichotomous Ordinal Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 9:1-9:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{angelini_et_al:LIPIcs.SoCG.2025.9,
  author =	{Angelini, Patrizio and Cornelsen, Sabine and Haase, Carolina and Hoffmann, Michael and Katsanou, Eleni and Montecchiani, Fabrizio and Steiner, Raphael and Symvonis, Antonios},
  title =	{{Geometric Realizations of Dichotomous Ordinal Graphs}},
  booktitle =	{41st International Symposium on Computational Geometry (SoCG 2025)},
  pages =	{9:1--9:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-370-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{332},
  editor =	{Aichholzer, Oswin and Wang, Haitao},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2025.9},
  URN =		{urn:nbn:de:0030-drops-231616},
  doi =		{10.4230/LIPIcs.SoCG.2025.9},
  annote =	{Keywords: Ordinal embeddings, geometric graphs, graph representations}
}
Document
DOI: 10.4230/LIPIcs.FUN.2022.14
The Synchronization Game on Subclasses of Automata

Authors: Henning Fernau, Carolina Haase, and Stefan Hoffmann

Published in: LIPIcs, Volume 226, 11th International Conference on Fun with Algorithms (FUN 2022)

Abstract
The notion of synchronization of finite automata is connected to one of the long-standing open problems in combinatorial automata theory, which is Černý’s Conjecture. In this paper, we focus on so-called synchronization games. We will discuss how to present synchronization questions in a playful way. This leads us to study related complexity questions on certain classes of finite automata. More precisely, we consider weakly acyclic, commutative and k-simple idempotent automata. We encounter a number of complexity classes, ranging from L up to PSPACE.
Cite as

Henning Fernau, Carolina Haase, and Stefan Hoffmann. The Synchronization Game on Subclasses of Automata. In 11th International Conference on Fun with Algorithms (FUN 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 226, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{fernau_et_al:LIPIcs.FUN.2022.14,
  author =	{Fernau, Henning and Haase, Carolina and Hoffmann, Stefan},
  title =	{{The Synchronization Game on Subclasses of Automata}},
  booktitle =	{11th International Conference on Fun with Algorithms (FUN 2022)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-232-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{226},
  editor =	{Fraigniaud, Pierre and Uno, Yushi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FUN.2022.14},
  URN =		{urn:nbn:de:0030-drops-159842},
  doi =		{10.4230/LIPIcs.FUN.2022.14},
  annote =	{Keywords: Synchronization of finite automata, computational complexity}
}
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