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Documents authored by Nikabadi, Amir

Document
DOI: 10.4230/LIPIcs.ESA.2025.40
Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs

Authors: Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We show that, for every fixed positive integers r and k, Max-Weight List r-Colorable Induced Subgraph admits a polynomial-time algorithm on kP₃-free graphs. This problem is a common generalization of Max-Weight Independent Set, Odd Cycle Transversal and List r-Coloring, among others. Our result has several consequences. First, it implies that, for every fixed r ≥ 5, assuming 𝖯 ≠ NP, Max-Weight List r-Colorable Induced Subgraph is polynomial-time solvable on H-free graphs if and only if H is an induced subgraph of either kP₃ or P₅+kP₁, for some k ≥ 1. Second, it makes considerable progress toward a complexity dichotomy for Odd Cycle Transversal on H-free graphs, allowing to answer a question of Agrawal, Lima, Lokshtanov, Rzążewski, Saurabh, and Sharma [ACM Trans. Algorithms 2025]. Third, it gives a short and self-contained proof of the known result of Chudnovsky, Hajebi, and Spirkl [Combinatorica 2024] that List r-Coloring on kP₃-free graphs is polynomial-time solvable for every fixed r and k. We also consider two natural distance-d generalizations of Max-Weight Independent Set and List r-Coloring and provide polynomial-time algorithms on kP₃-free graphs for every fixed integers r, k, and d ≥ 6.
Cite as

Esther Galby, Paloma T. Lima, Andrea Munaro, and Amir Nikabadi. Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 40:1-40:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{galby_et_al:LIPIcs.ESA.2025.40,
  author =	{Galby, Esther and Lima, Paloma T. and Munaro, Andrea and Nikabadi, Amir},
  title =	{{Maximum List r-Colorable Induced Subgraphs in kP₃-Free Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{40:1--40:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.40},
  URN =		{urn:nbn:de:0030-drops-245086},
  doi =		{10.4230/LIPIcs.ESA.2025.40},
  annote =	{Keywords: Hereditary classes, list coloring, odd cycle transversal, independent set}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2021.15
Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters

Authors: Amir Nikabadi and Janne H. Korhonen

Published in: LIPIcs, Volume 217, 25th International Conference on Principles of Distributed Systems (OPODIS 2021)

Abstract
Subgraph detection has recently been one of the most studied problems in the CONGEST model of distributed computing. In this work, we study the distributed complexity of problems closely related to subgraph detection, mainly focusing on induced subgraph detection. The main line of this work presents lower bounds and parameterized algorithms w.r.t structural parameters of the input graph: - On general graphs, we give unconditional lower bounds for induced detection of cycles and patterns of treewidth 2 in CONGEST. Moreover, by adapting reductions from centralized parameterized complexity, we prove lower bounds in CONGEST for detecting patterns with a 4-clique, and for induced path detection conditional on the hardness of triangle detection in the congested clique. - On graphs of bounded degeneracy, we show that induced paths can be detected fast in CONGEST using techniques from parameterized algorithms, while detecting cycles and patterns of treewidth 2 is hard. - On graphs of bounded vertex cover number, we show that induced subgraph detection is easy in CONGEST for any pattern graph. More specifically, we adapt a centralized parameterized algorithm for a more general maximum common induced subgraph detection problem to the distributed setting. In addition to these induced subgraph detection results, we study various related problems in the CONGEST and congested clique models, including for multicolored versions of subgraph-detection-like problems.
Cite as

Amir Nikabadi and Janne H. Korhonen. Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters. In 25th International Conference on Principles of Distributed Systems (OPODIS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 217, pp. 15:1-15:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{nikabadi_et_al:LIPIcs.OPODIS.2021.15,
  author =	{Nikabadi, Amir and Korhonen, Janne H.},
  title =	{{Beyond Distributed Subgraph Detection: Induced Subgraphs, Multicolored Problems and Graph Parameters}},
  booktitle =	{25th International Conference on Principles of Distributed Systems (OPODIS 2021)},
  pages =	{15:1--15:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-219-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{217},
  editor =	{Bramas, Quentin and Gramoli, Vincent and Milani, Alessia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2021.15},
  URN =		{urn:nbn:de:0030-drops-157902},
  doi =		{10.4230/LIPIcs.OPODIS.2021.15},
  annote =	{Keywords: distributed algorithms, parameterized distributed complexity, CONGEST model, induced subgraph detection, graph parameters, lower bounds}
}
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