The Complexity of L(p, q)-Edge-Labelling (2023)
Journal Article
Berthe, G., Martin, B., Paulusma, D., & Smith, S. (2023). The Complexity of L(p, q)-Edge-Labelling. Algorithmica, https://doi.org/10.1007/s00453-023-01120-4

The L(p, q)-EDGE-LABELLING problem is the edge variant of the well-known L(p, q)-LABELLING problem. It is equivalent to the L(p, q)-LABELLING problem itself if we restrict the input of the latter problem to line graphs. So far, the complexity of L(p,... Read More about The Complexity of L(p, q)-Edge-Labelling.

Induced Disjoint Paths and Connected Subgraphs for H-Free Graphs (2023)
Journal Article
Martin, B., Paulusma, D., Smith, S., & van Leeuwen, E. J. (2023). Induced Disjoint Paths and Connected Subgraphs for H-Free Graphs. Algorithmica, 85, 2580–2604. https://doi.org/10.1007/s00453-023-01109-z

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. The INDUCED DISJOINT PATHS problem is to decide if a graph G with k pairs of specified vertices (si,ti) contains k... Read More about Induced Disjoint Paths and Connected Subgraphs for H-Free Graphs.

Few induced disjoint paths for H-free graphs (2022)
Journal Article
Martin, B., Paulusma, D., Smith, S., & van Leeuwen, E. (2023). Few induced disjoint paths for H-free graphs. Theoretical Computer Science, 939, 182-193. https://doi.org/10.1016/j.tcs.2022.10.024

Paths in a graph are mutually induced if any two distinct and have neither common vertices nor adjacent vertices. For a fixed integer k, the k-Induced Disjoint Paths problem is to decide if a graph G with k pairs of specified vertices contains k mutu... Read More about Few induced disjoint paths for H-free graphs.

Feedback Vertex Set and Even Cycle Transversal for H-free graphs: Finding large block graphs (2022)
Journal Article
Paesani, G., Paulusma, D., & Rzążwski, P. (2022). Feedback Vertex Set and Even Cycle Transversal for H-free graphs: Finding large block graphs. SIAM Journal on Discrete Mathematics, 36(4), 2453-2472. https://doi.org/10.1137/22m1468864

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 for every s \geq 1, both problems are pol... Read More about Feedback Vertex Set and Even Cycle Transversal for H-free graphs: Finding large block graphs.

On the complexity of matching cut for graphs of bounded radius and H-free graphs (2022)
Journal Article
Lucke, F., Paulusma, D., & Ries, B. (2022). On the complexity of matching cut for graphs of bounded radius and H-free graphs. Theoretical Computer Science, 936, 33-42. https://doi.org/10.1016/j.tcs.2022.09.014

For a connected graph G = (V , E), a matching M ⊆ E is a matching cut of G if G − M is disconnected. It is known that for an integer d, the corresponding decision problem Matching Cut is polynomial-time solvable for graphs of diameter at most d if d... Read More about On the complexity of matching cut for graphs of bounded radius and H-free graphs.

Colouring generalized claw-free graphs and graphs of large girth: Bounding the diameter (2022)
Journal Article
Martin, B., Paulusma, D., & Smith, S. (2022). Colouring generalized claw-free graphs and graphs of large girth: Bounding the diameter. Theoretical Computer Science, 931, 104-116. https://doi.org/10.1016/j.tcs.2022.07.034

For a fixed integer, the k-Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for an integer k, such that no two adjacent vertices are coloured alike. A graph G is H-free if G does not contain H as an ind... Read More about Colouring generalized claw-free graphs and graphs of large girth: Bounding the diameter.

Partitioning H-free graphs of bounded diameter (2022)
Journal Article
Brause, C., Golovach, P., Martin, B., Paulusma, D., & Smith, S. (2022). Partitioning H-free graphs of bounded diameter. Theoretical Computer Science, 930, 37-52. https://doi.org/10.1016/j.tcs.2022.07.009

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.

Acyclic, Star, and Injective Colouring: Bounding the diameter (2022)
Journal Article
Brause, C., Golovach, P., Martin, B., Ochem, P., Paulusma, D., & Smith, S. (2022). Acyclic, Star, and Injective Colouring: Bounding the diameter. Electronic Journal of Combinatorics, 29(2), https://doi.org/10.37236/10738

We examine the effect of bounding the diameter for a number of natural and well-studied 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... Read More about Acyclic, Star, and Injective Colouring: Bounding the diameter.

Computing weighted subset odd cycle transversals in H-free graphs (2022)
Journal Article
Brettell, N., Johnson, M., & Paulusma, D. (2022). Computing weighted subset odd cycle transversals in H-free graphs. Journal of Computer and System Sciences, 128, 71-85. https://doi.org/10.1016/j.jcss.2022.03.002

For the Odd Cycle Transversal problem, the task is to find a small set S of vertices in a graph that intersects every cycle of odd length. The Subset Odd Cycle Transversal problem requires S to intersect only those odd cycles that include a vertex of... Read More about Computing weighted subset odd cycle transversals in H-free graphs.

QCSP on reflexive tournaments (2022)
Journal Article
Larose, B., Martin, B., Markovic, P., Paulusma, D., Smith, S., & Zivny, S. (2022). QCSP on reflexive tournaments. ACM Transactions on Computational Logic, 23(3), 1-22. https://doi.org/10.1145/3508069

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 that ther... Read More about QCSP on reflexive tournaments.

Colouring graphs of bounded diameter in the absence of small cycles (2022)
Journal Article
Martin, B., Paulusma, D., & Smith, S. (2022). Colouring graphs of bounded diameter in the absence of small cycles. Discrete Applied Mathematics, 314, 150-161. https://doi.org/10.1016/j.dam.2022.02.026

For k ≥ 1, a k-colouring c of G is a mapping from V (G) to {1, 2, . . . , k} such that c(u) 6= c(v) for any two adjacent vertices u and v. The k-Colouring problem is to decide if a graph G has a k-colouring. For a family of graphs H, a graph G is H-f... Read More about Colouring graphs of bounded diameter in the absence of small cycles.

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.

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.

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.

List k-colouring P-free graphs: a mim-width perspective (2021)
Journal Article
Brettell, N., Horsfield, J., Munaro, A., & Paulusma, D. (2022). List k-colouring P-free graphs: a mim-width perspective. Information Processing Letters, 173, Article 106168. https://doi.org/10.1016/j.ipl.2021.106168

A colouring of a graph G = (V, E) is a mapping c : V → {1, 2, . . .} such that c(u) 6= c(v) for every two adjacent vertices u and v of G. The List k-Colouring problem is to decide whether a graph G = (V, E) with a list L(u) ⊆ {1, . . . , k} for each... Read More about List k-colouring P-free graphs: a mim-width perspective.

Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration (2021)
Journal Article
Bonamy, M., Dabrowski, K., Feghali, C., Johnson, M., & Paulusma, D. (2021). Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration. Journal of Graph Theory, 98(1), 81-109. https://doi.org/10.1002/jgt.22683

We continue research into a well-studied family of problems that ask whether the vertices of a given graph can be partitioned into sets A and B, where A is an independent set and B induces a graph from some specified graph class G. We consider the ca... Read More about Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration.

What graphs are 2-dot product graphs? (2021)
Journal Article
Johnson, M., Paulusma, D., & van Leeuwen, E. (2021). What graphs are 2-dot product graphs?. International Journal of Computational Geometry and Applications, 31(01), 1-16. https://doi.org/10.1142/s0218195921500011

Let d ≥ 1 be an integer. From a set of d-dimensional vectors, we obtain a d-dot product graph by letting each vector a u correspond to a vertex u and by adding an edge between two vertices u and v if and only if their dot product a u · a v ≥ t, for s... Read More about What graphs are 2-dot product graphs?.