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

Given a graph G, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of G that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in literature, has been intensively studied, enumeration algorithms were only known for a few simple graph classes, e.g., independent sets, cliques, and forests, until very recently [Conte and Uno, STOC 2019]. There is also a connected variation of this problem, where one is concerned with only those induced subgraphs that are connected. We introduce two new approaches, which enable us to develop algorithms that solve both variations for a number of important graph classes. A general technique that has been proven very powerful in enumeration algorithms is to build a solution map, i.e., a multiple digraph on all the solutions of the problem, and the key of this approach is to make the solution map strongly connected, so that a simple traversal of the solution map solves the problem. First, we introduce retaliation-free paths to certify strong connectedness of the solution map we build. Second, generalizing the idea of Cohen, Kimelfeld, and Sagiv [JCSS 2008], we introduce an apparently very restricted version of the maximal (connected) induced subgraphs problem, and show that it is equivalent to the original problem in terms of solvability in incremental polynomial time. Moreover, we give reductions between the two variations, so that it suffices to solve one of the variations for each class we study. Our work also leads to direct and simpler proofs of several important known results.

Yixin Cao. Enumerating Maximal Induced Subgraphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 31:1-31:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cao:LIPIcs.ESA.2023.31, author = {Cao, Yixin}, title = {{Enumerating Maximal Induced Subgraphs}}, booktitle = {31st Annual European Symposium on Algorithms (ESA 2023)}, pages = {31:1--31:13}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.31}, URN = {urn:nbn:de:0030-drops-186841}, doi = {10.4230/LIPIcs.ESA.2023.31}, annote = {Keywords: enumeration algorithm, hereditary graph class, maximal induced subgraph} }

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

We present a 9^k ⋅ n^O(1)-time algorithm for the proper circular-arc vertex deletion problem, resolving an open problem of van ’t Hof and Villanger [Algorithmica 2013] and Crespelle et al. [Computer Science Review 2023]. Our structural study also implies parameterized algorithms for modification problems toward proper Helly circular-arc graphs.

Yixin Cao, Hanchun Yuan, and Jianxin Wang. Modification Problems Toward Proper (Helly) Circular-Arc Graphs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cao_et_al:LIPIcs.MFCS.2023.31, author = {Cao, Yixin and Yuan, Hanchun and Wang, Jianxin}, title = {{Modification Problems Toward Proper (Helly) Circular-Arc Graphs}}, booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)}, pages = {31:1--31:14}, 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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.31}, URN = {urn:nbn:de:0030-drops-185652}, doi = {10.4230/LIPIcs.MFCS.2023.31}, annote = {Keywords: proper (Helly) circular-arc graph, graph modification problem} }

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**Published in:** LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

In an edge modification problem, we are asked to modify at most k edges of a given graph to make the graph satisfy a certain property. Depending on the operations allowed, we have the completion problems and the edge deletion problems. A great amount of efforts have been devoted to understanding the kernelization complexity of these problems. We revisit several well-studied edge modification problems, and develop improved kernels for them:
- a 2 k-vertex kernel for the cluster edge deletion problem,
- a 3 k²-vertex kernel for the trivially perfect completion problem,
- a 5 k^{1.5}-vertex kernel for the split completion problem and the split edge deletion problem, and
- a 5 k^{1.5}-vertex kernel for the pseudo-split completion problem and the pseudo-split edge deletion problem. Moreover, our kernels for split completion and pseudo-split completion have only O(k^{2.5}) edges. Our results also include a 2 k-vertex kernel for the strong triadic closure problem, which is related to cluster edge deletion.

Yixin Cao and Yuping Ke. Improved Kernels for Edge Modification Problems. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cao_et_al:LIPIcs.IPEC.2021.13, author = {Cao, Yixin and Ke, Yuping}, title = {{Improved Kernels for Edge Modification Problems}}, booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)}, pages = {13:1--13:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-216-7}, ISSN = {1868-8969}, year = {2021}, volume = {214}, editor = {Golovach, Petr A. and Zehavi, Meirav}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.13}, URN = {urn:nbn:de:0030-drops-153965}, doi = {10.4230/LIPIcs.IPEC.2021.13}, annote = {Keywords: Kernelization, edge modification, cluster, trivially perfect graphs, split graphs} }

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Complete Volume

**Published in:** LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

LIPIcs, Volume 180, IPEC 2020, Complete Volume

15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 1-498, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{cao_et_al:LIPIcs.IPEC.2020, title = {{LIPIcs, Volume 180, IPEC 2020, Complete Volume}}, booktitle = {15th International Symposium on Parameterized and Exact Computation (IPEC 2020)}, pages = {1--498}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-172-6}, ISSN = {1868-8969}, year = {2020}, volume = {180}, editor = {Cao, Yixin and Pilipczuk, Marcin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020}, URN = {urn:nbn:de:0030-drops-133022}, doi = {10.4230/LIPIcs.IPEC.2020}, annote = {Keywords: LIPIcs, Volume 180, IPEC 2020, Complete Volume} }

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Front Matter

**Published in:** LIPIcs, Volume 180, 15th International Symposium on Parameterized and Exact Computation (IPEC 2020)

Front Matter, Table of Contents, Preface, Conference Organization

15th International Symposium on Parameterized and Exact Computation (IPEC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 180, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cao_et_al:LIPIcs.IPEC.2020.0, author = {Cao, Yixin and Pilipczuk, Marcin}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {15th International Symposium on Parameterized and Exact Computation (IPEC 2020)}, pages = {0:i--0:xviii}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-172-6}, ISSN = {1868-8969}, year = {2020}, volume = {180}, editor = {Cao, Yixin and Pilipczuk, Marcin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2020.0}, URN = {urn:nbn:de:0030-drops-133035}, doi = {10.4230/LIPIcs.IPEC.2020.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

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Complete Volume

**Published in:** LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

LIPIcs, Volume 181, ISAAC 2020, Complete Volume

31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 1-1012, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@Proceedings{cao_et_al:LIPIcs.ISAAC.2020, title = {{LIPIcs, Volume 181, ISAAC 2020, Complete Volume}}, booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)}, pages = {1--1012}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-173-3}, ISSN = {1868-8969}, year = {2020}, volume = {181}, editor = {Cao, Yixin and Cheng, Siu-Wing and Li, Minming}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020}, URN = {urn:nbn:de:0030-drops-133439}, doi = {10.4230/LIPIcs.ISAAC.2020}, annote = {Keywords: LIPIcs, Volume 181, ISAAC 2020, Complete Volume} }

Document

Front Matter

**Published in:** LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

Front Matter, Table of Contents, Preface, Conference Organization

31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cao_et_al:LIPIcs.ISAAC.2020.0, author = {Cao, Yixin and Cheng, Siu-Wing and Li, Minming}, title = {{Front Matter, Table of Contents, Preface, Conference Organization}}, booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)}, pages = {0:i--0:xviii}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-173-3}, ISSN = {1868-8969}, year = {2020}, volume = {181}, editor = {Cao, Yixin and Cheng, Siu-Wing and Li, Minming}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.0}, URN = {urn:nbn:de:0030-drops-133448}, doi = {10.4230/LIPIcs.ISAAC.2020.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Conference Organization} }

Document

**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Graph search, the process of visiting vertices in a graph in a specific order, has demonstrated magical powers in many important algorithms. But a systematic study was only initiated by Corneil et al. a decade ago, and only by then we started to realize how little we understand it. Even the apparently naïve question "which vertex can be the last visited by a graph search algorithm," known as the end vertex problem, turns out to be quite elusive. We give a full picture of all maximum cardinality searches on chordal graphs, which implies a polynomial-time algorithm for the end vertex problem of maximum cardinality search. It is complemented by a proof of NP-completeness of the same problem on weakly chordal graphs. We also show linear-time algorithms for deciding end vertices of breadth-first searches on interval graphs, and end vertices of lexicographic depth-first searches on chordal graphs. Finally, we present 2^n * n^O(1)-time algorithms for deciding the end vertices of breadth-first searches, depth-first searches, and maximum cardinality searches on general graphs.

Yixin Cao, Zhifeng Wang, Guozhen Rong, and Jianxin Wang. Graph Searches and Their End Vertices. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cao_et_al:LIPIcs.ISAAC.2019.1, author = {Cao, Yixin and Wang, Zhifeng and Rong, Guozhen and Wang, Jianxin}, title = {{Graph Searches and Their End Vertices}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {1:1--1:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.1}, URN = {urn:nbn:de:0030-drops-114973}, doi = {10.4230/LIPIcs.ISAAC.2019.1}, annote = {Keywords: maximum cardinality search, (lexicographic) breadth-first search, (lexicographic) depth-first search, chordal graph, weighted clique graph, end vertex} }

Document

**Published in:** LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Given a fixed graph H, the H-free editing problem asks whether we can edit at most k edges to make a graph contain no induced copy of H. We obtain a polynomial kernel for this problem when H is a diamond. The incompressibility dichotomy for H being a 3-connected graph and the classical complexity dichotomy suggest that except for H being a complete/empty graph, H-free editing problems admit polynomial kernels only for a few small graphs H. Therefore, we believe that our result is an essential step toward a complete dichotomy on the compressibility of H-free editing. Additionally, we give a cubic-vertex kernel for the diamond-free edge deletion problem, which is far simpler than the previous kernel of the same size for the problem.

Yixin Cao, Ashutosh Rai, R. B. Sandeep, and Junjie Ye. A Polynomial Kernel for Diamond-Free Editing. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cao_et_al:LIPIcs.ESA.2018.10, author = {Cao, Yixin and Rai, Ashutosh and Sandeep, R. B. and Ye, Junjie}, title = {{A Polynomial Kernel for Diamond-Free Editing}}, booktitle = {26th Annual European Symposium on Algorithms (ESA 2018)}, pages = {10:1--10:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-081-1}, ISSN = {1868-8969}, year = {2018}, volume = {112}, editor = {Azar, Yossi and Bast, Hannah and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.10}, URN = {urn:nbn:de:0030-drops-94732}, doi = {10.4230/LIPIcs.ESA.2018.10}, annote = {Keywords: Kernelization, Diamond-free, H-free editing, Graph modification problem} }

Document

**Published in:** LIPIcs, Volume 93, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)

Containing many classic optimization problems, the family of vertex deletion problems has an important position in algorithm and complexity study. The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity. It however has nothing to say about the case when the input graph is also special. This paper initiates a systematic study of vertex deletion problems from one subclass of chordal graphs to another. We give polynomial-time algorithms or proofs of NP-completeness for most of the problems. In particular, we show that the vertex deletion problem from chordal graphs to interval graphs is NP-complete.

Yixin Cao, Yuping Ke, Yota Otachi, and Jie You. Vertex Deletion Problems on Chordal Graphs. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 22:1-22:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cao_et_al:LIPIcs.FSTTCS.2017.22, author = {Cao, Yixin and Ke, Yuping and Otachi, Yota and You, Jie}, title = {{Vertex Deletion Problems on Chordal Graphs}}, booktitle = {37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)}, pages = {22:1--22:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-055-2}, ISSN = {1868-8969}, year = {2018}, volume = {93}, editor = {Lokam, Satya and Ramanujam, R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2017.22}, URN = {urn:nbn:de:0030-drops-83799}, doi = {10.4230/LIPIcs.FSTTCS.2017.22}, annote = {Keywords: vertex deletion problem, maximum subgraph, chordal graph, (unit) interval graph, split graph, hereditary property, NP-complete, polynomial-time algori} }

Document

**Published in:** OASIcs, Volume 61, 1st Symposium on Simplicity in Algorithms (SOSA 2018)

Given a graph on n vertices and an integer k, the feedback vertex set problem asks for the deletion of at most k vertices to make the graph acyclic. We show that a greedy branching algorithm, which always branches on an undecided vertex with the largest degree, runs in single-exponential time, i.e., O(c^k n^2) for some constant c.

Yixin Cao. A Naive Algorithm for Feedback Vertex Set. In 1st Symposium on Simplicity in Algorithms (SOSA 2018). Open Access Series in Informatics (OASIcs), Volume 61, pp. 1:1-1:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cao:OASIcs.SOSA.2018.1, author = {Cao, Yixin}, title = {{A Naive Algorithm for Feedback Vertex Set}}, booktitle = {1st Symposium on Simplicity in Algorithms (SOSA 2018)}, pages = {1:1--1:9}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-064-4}, ISSN = {2190-6807}, year = {2018}, volume = {61}, editor = {Seidel, Raimund}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2018.1}, URN = {urn:nbn:de:0030-drops-82961}, doi = {10.4230/OASIcs.SOSA.2018.1}, annote = {Keywords: greedy algorithm, analysis of algorithms, branching algorithm, parameterized computation -- graph modification problem} }

Document

**Published in:** LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Graph modification problems are typically asked as follows: is there a set of k operations that transforms a given graph to have a certain property. The most commonly considered operations include vertex deletion, edge deletion, and edge addition; for the same property, one can define significantly different versions by allowing different operations. We study a very general graph modification problem which allows all three types of operations: given a graph G and integers k_1, k_2, and k_3, the CHORDAL EDITING problem asks if G can be transformed into a chordal graph by at most k_1 vertex deletions, k_2 edge deletions, and k_3 edge additions. Clearly, this problem generalizes both CHORDAL VERTEX/EDGE DELETION and CHORDAL COMPLETION (also known as MINIMUM FILL-IN). Our main result is an algorithm for CHORDAL EDITING in time 2^O(k.log(k))·n^O(1), where k:=k_1+k_2+k_3; therefore, the problem is fixed-parameter tractable parameterized by the total number of allowed operations. Our algorithm is both more efficient and conceptually simpler than the previously known algorithm for the special case CHORDAL DELETION.

Yixin Cao and Dániel Marx. Chordal Editing is Fixed-Parameter Tractable. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 214-225, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{cao_et_al:LIPIcs.STACS.2014.214, author = {Cao, Yixin and Marx, D\'{a}niel}, title = {{Chordal Editing is Fixed-Parameter Tractable}}, booktitle = {31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)}, pages = {214--225}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-65-1}, ISSN = {1868-8969}, year = {2014}, volume = {25}, editor = {Mayr, Ernst W. and Portier, Natacha}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.214}, URN = {urn:nbn:de:0030-drops-44591}, doi = {10.4230/LIPIcs.STACS.2014.214}, annote = {Keywords: chordal graph, parameterized computation, graph modification problems, chordal deletion, chordal completion, clique tree decomposition, holes, simplic} }

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