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Documents authored by Baligács, Júlia

Document
DOI: 10.4230/LIPIcs.MFCS.2025.15
Symmetry Classes of Hamiltonian Cycles

Authors: Júlia Baligács, Sofia Brenner, Annette Lutz, and Lena Volk

Published in: LIPIcs, Volume 345, 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)

Abstract
We initiate the study of Hamiltonian cycles up to symmetries of the underlying graph. Our focus lies on the extremal case of Hamiltonian-transitive graphs, i.e., Hamiltonian graphs where, for every pair of Hamiltonian cycles, there is a graph automorphism mapping one cycle to the other. This generalizes the extensively studied uniquely Hamiltonian graphs. In this paper, we show that Cayley graphs of abelian groups are not Hamiltonian-transitive (under some mild conditions and some non-surprising exceptions), i.e., they contain at least two structurally different Hamiltonian cycles. To show this, we reduce Hamiltonian-transitivity to properties of the prime factors of a Cartesian product decomposition, which we believe is interesting in its own right. We complement our results by constructing infinite families of regular Hamiltonian-transitive graphs and take a look at the opposite extremal case by constructing a family with many different Hamiltonian cycles up to symmetry.
Cite as

Júlia Baligács, Sofia Brenner, Annette Lutz, and Lena Volk. Symmetry Classes of Hamiltonian Cycles. In 50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 345, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baligacs_et_al:LIPIcs.MFCS.2025.15,
  author =	{Balig\'{a}cs, J\'{u}lia and Brenner, Sofia and Lutz, Annette and Volk, Lena},
  title =	{{Symmetry Classes of Hamiltonian Cycles}},
  booktitle =	{50th International Symposium on Mathematical Foundations of Computer Science (MFCS 2025)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-388-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{345},
  editor =	{Gawrychowski, Pawe{\l} and Mazowiecki, Filip and Skrzypczak, Micha{\l}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2025.15},
  URN =		{urn:nbn:de:0030-drops-241221},
  doi =		{10.4230/LIPIcs.MFCS.2025.15},
  annote =	{Keywords: Hamiltonian cycles, graph automorphisms, Cayley graphs, abelian groups, Cartesian product of graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.15
A (5/3+ε)-Approximation for Tricolored Non-Crossing Euclidean TSP

Authors: Júlia Baligács, Yann Disser, Andreas Emil Feldmann, and Anna Zych-Pawlewicz

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
In the Tricolored Euclidean Traveling Salesperson problem, we are given k = 3 sets of points in the plane and are looking for disjoint tours, each covering one of the sets. Arora (1998) famously gave a PTAS based on "patching" for the case k = 1 and, recently, Dross et al. (2023) generalized this result to k = 2. Our contribution is a (5/3+ε)-approximation algorithm for k = 3 that further generalizes Arora’s approach. It is believed that patching is generally no longer possible for more than two tours. We circumvent this issue by either applying a conditional patching scheme for three tours or using an alternative approach based on a weighted solution for k = 2.
Cite as

Júlia Baligács, Yann Disser, Andreas Emil Feldmann, and Anna Zych-Pawlewicz. A (5/3+ε)-Approximation for Tricolored Non-Crossing Euclidean TSP. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 15:1-15:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{baligacs_et_al:LIPIcs.ESA.2024.15,
  author =	{Balig\'{a}cs, J\'{u}lia and Disser, Yann and Feldmann, Andreas Emil and Zych-Pawlewicz, Anna},
  title =	{{A (5/3+\epsilon)-Approximation for Tricolored Non-Crossing Euclidean TSP}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{15:1--15:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.15},
  URN =		{urn:nbn:de:0030-drops-210862},
  doi =		{10.4230/LIPIcs.ESA.2024.15},
  annote =	{Keywords: Approximation Algorithms, geometric Network Optimization, Euclidean TSP, non-crossing Structures}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.11
Exploration of Graphs with Excluded Minors

Authors: Júlia Baligács, Yann Disser, Irene Heinrich, and Pascal Schweitzer

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
We study the online graph exploration problem proposed by Kalyanasundaram and Pruhs (1994) and prove a constant competitive ratio on minor-free graphs. This result encompasses and significantly extends the graph classes that were previously known to admit a constant competitive ratio. The main ingredient of our proof is that we find a connection between the performance of the particular exploration algorithm Blocking and the existence of light spanners. Conversely, we exploit this connection to construct light spanners of bounded genus graphs. In particular, we achieve a lightness that improves on the best known upper bound for genus g ≥ 1 and recovers the known tight bound for the planar case (g = 0).
Cite as

Júlia Baligács, Yann Disser, Irene Heinrich, and Pascal Schweitzer. Exploration of Graphs with Excluded Minors. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 11:1-11:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{baligacs_et_al:LIPIcs.ESA.2023.11,
  author =	{Balig\'{a}cs, J\'{u}lia and Disser, Yann and Heinrich, Irene and Schweitzer, Pascal},
  title =	{{Exploration of Graphs with Excluded Minors}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{11:1--11:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.11},
  URN =		{urn:nbn:de:0030-drops-186644},
  doi =		{10.4230/LIPIcs.ESA.2023.11},
  annote =	{Keywords: online algorithms, competitive analysis, graph exploration, graph spanners, minor-free graphs, bounded genus graphs}
}
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