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Documents authored by Lucke, Felicia

Document
DOI: 10.4230/LIPIcs.ISAAC.2023.31
Matching Cuts in Graphs of High Girth and H-Free Graphs

Authors: Carl Feghali, Felicia Lucke, Daniël Paulusma, and Bernard Ries

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
The (Perfect) Matching Cut problem is to decide if a connected graph has a (perfect) matching that is also an edge cut. The Disconnected Perfect Matching problem is to decide if a connected graph has a perfect matching that contains a matching cut. Both Matching Cut and Disconnected Perfect Matching are NP-complete for planar graphs of girth 5, whereas Perfect Matching Cut is known to be NP-complete even for subcubic bipartite graphs of arbitrarily large fixed girth. We prove that Matching Cut and Disconnected Perfect Matching are also NP-complete for bipartite graphs of arbitrarily large fixed girth and bounded maximum degree. Our result for Matching Cut resolves a 20-year old open problem. We also show that the more general problem d-Cut, for every fixed d ≥ 1, is NP-complete for bipartite graphs of arbitrarily large fixed girth and bounded maximum degree. Furthermore, we show that Matching Cut, Perfect Matching Cut and Disconnected Perfect Matching are NP-complete for H-free graphs whenever H contains a connected component with two vertices of degree at least 3. Afterwards, we update the state-of-the-art summaries for H-free graphs and compare them with each other, and with a known and full classification of the Maximum Matching Cut problem, which is to determine a largest matching cut of a graph G. Finally, by combining existing results, we obtain a complete complexity classification of Perfect Matching Cut for H-subgraph-free graphs where H is any finite set of graphs.
Cite as

Carl Feghali, Felicia Lucke, Daniël Paulusma, and Bernard Ries. Matching Cuts in Graphs of High Girth and H-Free Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 31:1-31:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{feghali_et_al:LIPIcs.ISAAC.2023.31,
  author =	{Feghali, Carl and Lucke, Felicia and Paulusma, Dani\"{e}l and Ries, Bernard},
  title =	{{Matching Cuts in Graphs of High Girth and H-Free Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{31:1--31:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.31},
  URN =		{urn:nbn:de:0030-drops-193332},
  doi =		{10.4230/LIPIcs.ISAAC.2023.31},
  annote =	{Keywords: matching cut, perfect matching, girth, H-free graph}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2023.64
Dichotomies for Maximum Matching Cut: H-Freeness, Bounded Diameter, Bounded Radius

Authors: Felicia Lucke, Daniël Paulusma, and Bernard Ries

Published in: LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

Abstract
The (Perfect) Matching Cut problem is to decide if a graph G has a (perfect) matching cut, i.e., a (perfect) matching that is also an edge cut of G. Both Matching Cut and Perfect Matching Cut are known to be NP-complete, leading to many complexity results for both problems on special graph classes. A perfect matching cut is also a matching cut with maximum number of edges. To increase our understanding of the relationship between the two problems, we introduce the Maximum Matching Cut problem. This problem is to determine a largest matching cut in a graph. We generalize and unify known polynomial-time algorithms for Matching Cut and Perfect Matching Cut restricted to graphs of diameter at most 2 and to (P₆+sP₂)-free graphs. We also show that the complexity of Maximum Matching Cut differs from the complexities of Matching Cut and Perfect Matching Cut by proving NP-hardness of Maximum Matching Cut for 2P₃-free quadrangulated graphs of diameter 3 and radius 2 and for subcubic line graphs of triangle-free graphs. In this way, we obtain full dichotomies of Maximum Matching Cut for graphs of bounded diameter, bounded radius and H-free graphs.
Cite as

Felicia Lucke, Daniël Paulusma, and Bernard Ries. Dichotomies for Maximum Matching Cut: H-Freeness, Bounded Diameter, Bounded Radius. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 64:1-64:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{lucke_et_al:LIPIcs.MFCS.2023.64,
  author =	{Lucke, Felicia and Paulusma, Dani\"{e}l and Ries, Bernard},
  title =	{{Dichotomies for Maximum Matching Cut: H-Freeness, Bounded Diameter, Bounded Radius}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{64:1--64:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.64},
  URN =		{urn:nbn:de:0030-drops-185981},
  doi =		{10.4230/LIPIcs.MFCS.2023.64},
  annote =	{Keywords: matching cut, perfect matching, H-free graph, diameter, radius, dichotomy}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.22
Finding Matching Cuts in H-Free Graphs

Authors: Felicia Lucke, Daniël Paulusma, and Bernard Ries

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
The well-known NP-complete problem Matching Cut is to decide if a graph has a matching that is also an edge cut of the graph. We prove new complexity results for Matching Cut restricted to H-free graphs, that is, graphs that do not contain some fixed graph H as an induced subgraph. We also prove new complexity results for two recently studied variants of Matching Cut, on H-free graphs. The first variant requires that the matching cut must be extendable to a perfect matching of the graph. The second variant requires the matching cut to be a perfect matching. In particular, we prove that there exists a small constant r > 0 such that the first variant is NP-complete for P_r-free graphs. This addresses a question of Bouquet and Picouleau (arXiv, 2020). For all three problems, we give state-of-the-art summaries of their computational complexity for H-free graphs.
Cite as

Felicia Lucke, Daniël Paulusma, and Bernard Ries. Finding Matching Cuts in H-Free Graphs. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lucke_et_al:LIPIcs.ISAAC.2022.22,
  author =	{Lucke, Felicia and Paulusma, Dani\"{e}l and Ries, Bernard},
  title =	{{Finding Matching Cuts in H-Free Graphs}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.22},
  URN =		{urn:nbn:de:0030-drops-173076},
  doi =		{10.4230/LIPIcs.ISAAC.2022.22},
  annote =	{Keywords: matching cut, perfect matching, H-free graph, computational complexity}
}
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