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Documents authored by Kim, Gunwoo

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2026.64
Odd-Cycle-Packing-Treewidth: On the Maximum Independent Set Problem in Odd-Minor-Free Graph Classes

Authors: Mujin Choi, Maximilian Gorsky, Gunwoo Kim, Caleb McFarland, and Sebastian Wiederrecht

Published in: LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)

Abstract
We introduce the tree-decomposition-based graph parameter Odd-Cycle-Packing-treewidth (OCP-tw) as a width parameter that asks to decompose a given graph into pieces of bounded odd cycle packing number. The parameter OCP-tw is monotone under the odd-minor-relation and we provide an analogue to the celebrated Grid Theorem of Robertson and Seymour for OCP-tw. That is, we identify two infinite families of grid-like graphs whose presence as odd-minors implies large OCP-tw and prove that their absence implies bounded OCP-tw. This structural result is constructive and implies a 2^poly(k) poly(n)-time parameterized poly(k)-approximation algorithm for OCP-tw. Moreover, we show that the (weighted) Maximum Independent Set problem (MIS) can be solved in polynomial time on graphs of bounded OCP-tw. Finally, we lift the concept of OCP-tw to a parameter for matrices of integer programs. To this end, we show that our strategy can be applied to efficiently solve integer programs whose matrices have entries in {-1,0,1} and can be "tree-decomposed" into totally Δ-modular matrices with at most two non-zero entries per row.
Cite as

Mujin Choi, Maximilian Gorsky, Gunwoo Kim, Caleb McFarland, and Sebastian Wiederrecht. Odd-Cycle-Packing-Treewidth: On the Maximum Independent Set Problem in Odd-Minor-Free Graph Classes. In 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 374, pp. 64:1-64:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{choi_et_al:LIPIcs.ICALP.2026.64,
  author =	{Choi, Mujin and Gorsky, Maximilian and Kim, Gunwoo and McFarland, Caleb and Wiederrecht, Sebastian},
  title =	{{Odd-Cycle-Packing-Treewidth: On the Maximum Independent Set Problem in Odd-Minor-Free Graph Classes}},
  booktitle =	{53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026)},
  pages =	{64:1--64:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-428-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{374},
  editor =	{Bhattacharya, Sayan and Nanongkai, Danupon and Benedikt, Michael and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.64},
  URN =		{urn:nbn:de:0030-drops-264533},
  doi =		{10.4230/LIPIcs.ICALP.2026.64},
  annote =	{Keywords: Odd-minor, treewidth, parameterized algorithm, graph minor, structural graph theory, Odd-Cycle-Packing-treewidth, Maximum Independent Set problem}
}
Document
DOI: 10.4230/LIPIcs.SoCG.2026.51
First-Order Logic and Twin-Width for Some Geometric Graphs

Authors: Colin Geniet, Gunwoo Kim, and Lucas Meijer

Published in: LIPIcs, Volume 367, 42nd International Symposium on Computational Geometry (SoCG 2026)

Abstract
For some geometric graph classes, tractability of testing first-order formulas is precisely characterised by the graph parameter twin-width. This was first proved for interval graphs among others in [BCKKLT, IPEC '22], where the equivalence is called delineation, and more generally holds for circle graphs, rooted directed path graphs, and H-graphs when H is a forest. Delineation is based on the key idea that geometric graphs often admit natural vertex orderings, allowing to use the very rich theory of twin-width for ordered graphs. Answering two questions raised in their work, we prove that delineation holds for intersection graphs of non-degenerate axis-parallel unit segment graphs, but fails for visibility graphs of 1.5D terrains. We also prove delineation for intersection graphs of circular arcs.
Cite as

Colin Geniet, Gunwoo Kim, and Lucas Meijer. First-Order Logic and Twin-Width for Some Geometric Graphs. In 42nd International Symposium on Computational Geometry (SoCG 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 367, pp. 51:1-51:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{geniet_et_al:LIPIcs.SoCG.2026.51,
  author =	{Geniet, Colin and Kim, Gunwoo and Meijer, Lucas},
  title =	{{First-Order Logic and Twin-Width for Some Geometric Graphs}},
  booktitle =	{42nd International Symposium on Computational Geometry (SoCG 2026)},
  pages =	{51:1--51:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-418-5},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{367},
  editor =	{Ahn, Hee-Kap and Hoffmann, Michael and Nayyeri, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2026.51},
  URN =		{urn:nbn:de:0030-drops-258575},
  doi =		{10.4230/LIPIcs.SoCG.2026.51},
  annote =	{Keywords: Twin-width, axis-parallel unit segment graphs, circular arc graphs, terrain visibility graphs, first-order logic, model checking, FPT}
}
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