Outputs (311)

Computing subset transversals in H-free graphs (2021)
Journal Article
Brettell, N., Johnson, M., Paesani, G., & Paulusma, D. (2022). Computing subset transversals in H-free graphs. Theoretical Computer Science, 902, 76-92. https://doi.org/10.1016/j.tcs.2021.12.010

we study the computational complexity of two well-known graph transversal problems, namely Subset Feedback Vertex Set and Subset Odd Cycle Transversal, by restricting the input to H-free graphs, that is, to graphs that do not contain some fixed graph... Read More about Computing subset transversals in H-free graphs.

Tree pivot-minors and linear rank-width (2021)
Journal Article
Dabrowski, K., Dross, F., Jeong, J., Kante, M., Kwon, O., Oum, S., & Paulusma, D. (2021). Tree pivot-minors and linear rank-width. SIAM Journal on Discrete Mathematics, 35(4), 2922-2945. https://doi.org/10.1137/21m1402339

Tree-width and its linear variant path-width play a central role for the graph minor relation. In particular, Robertson and Seymour (1983) proved that for every tree T, the class of graphs that do not contain T as a minor has bounded path-width. For... Read More about Tree pivot-minors and linear rank-width.

Partitioning H-free graphs of bounded diameter (2021)
Presentation / Conference Contribution
Brause, C., Golovach, P. A., Martin, B., Paulusma, D., & Smith, S. (2021, December). Partitioning H-free graphs of bounded diameter. Presented at 32nd International Symposium on Algorithms and Computation (ISAAC 2021), Fukuoka, Japan

A natural way of increasing our understanding of NP-complete graph problems is to restrict the input to a special graph class. Classes of H-free graphs, that is, graphs that do not contain some graph H as an induced subgraph, have proven to be an ide... Read More about Partitioning H-free graphs of bounded diameter.

Induced disjoint paths in AT-free graphs (2021)
Journal Article
Golovach, P., Paulusma, D., & van Leeuwen, E. (2022). Induced disjoint paths in AT-free graphs. Journal of Computer and System Sciences, 124, 170-191. https://doi.org/10.1016/j.jcss.2021.10.003

Paths P1, . . . , Pk in a graph G = (V, E) are mutually induced if any two distinct Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their end-vertices). The Induced Disjoint Paths problem is to decide if a graph G with k... Read More about Induced disjoint paths in AT-free graphs.

Disjoint paths and connected subgraphs for H-free graphs (2021)
Journal Article
Kern, W., Martin, B., Paulusma, D., Smith, S., & van Leeuwen, E. (2022). Disjoint paths and connected subgraphs for H-free graphs. Theoretical Computer Science, 898, 59-68. https://doi.org/10.1016/j.tcs.2021.10.019

The well-known Disjoint Paths problem is to decide if a graph contains k pairwise disjoint paths, each connecting a different terminal pair from a set of k distinct vertex pairs. We determine, with an exception of two cases, the complexity of the Dis... Read More about Disjoint paths and connected subgraphs for H-free graphs.

Hard problems that quickly become very easy (2021)
Journal Article
Martin, B., Paulusma, D., & Smith, S. (2022). Hard problems that quickly become very easy. Information Processing Letters, 174, https://doi.org/10.1016/j.ipl.2021.106213

A graph class is hereditary if it is closed under vertex deletion. We give examples of NP-hard, PSPACE-complete and NEXPTIME-complete problems that become constant-time solvable for every hereditary graph class that is not equal to the class of all g... Read More about Hard problems that quickly become very easy.

Acyclic, star and injective colouring: bounding the diameter (2021)
Presentation / Conference Contribution
Brause, C., Golovach, P., Martin, B., Paulusma, D., & Smith, S. Acyclic, star and injective colouring: bounding the diameter

We examine the effect of bounding the diameter for wellstudied variants of the Colouring problem. A colouring is acyclic, star, or injective if any two colour classes induce a forest, star forest or disjoint union of vertices and edges, respectively.... Read More about Acyclic, star and injective colouring: bounding the diameter.

QCSP on reflexive tournaments (2021)
Presentation / Conference Contribution
Larose, B., Markovic, P., Martin, B., Paulusma, D., Smith, S., & Zivny, S. (2021, September). QCSP on reflexive tournaments. Presented at The 29th Annual European Symposium on Algorithms (ESA 2021), Lisbon / Online

We give a complexity dichotomy for the Quantified Constraint Satisfaction Problem QCSP(H) when H is a reflexive tournament. It is well-known that reflexive tournaments can be split into a sequence of strongly connected components H1, . . . , Hn so th... Read More about QCSP on reflexive tournaments.

Bounding the mim-width of hereditary graph classes (2021)
Journal Article
Brettell, N., Horsfield, J., Munaro, A., Paesani, G., & Paulusma, D. (2022). Bounding the mim-width of hereditary graph classes. Journal of Graph Theory, 99(1), 117-151. https://doi.org/10.1002/jgt.22730

A large number of NP-hard graph problems are solvable in XP time when parameterized by some width parameter. Hence, when solving problems on special graph classes, it is helpful to know if the graph class under consideration has bounded width. In thi... Read More about Bounding the mim-width of hereditary graph classes.

Feedback Vertex Set and Even Cycle Transversal for H-free graphs: finding large block graphs (2021)
Presentation / Conference Contribution
Paesani, G., Paulusma, D., & Rzążewski, P. (2021, August). Feedback Vertex Set and Even Cycle Transversal for H-free graphs: finding large block graphs. Presented at MFCS 2021, Tallinn, Estonia

We prove new complexity results for Feedback Vertex Set and Even Cycle Transversal on H-free graphs, that is, graphs that do not contain some fixed graph H as an induced subgraph. In particular, we prove that both problems are polynomial-time solvabl... Read More about Feedback Vertex Set and Even Cycle Transversal for H-free graphs: finding large block graphs.