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.

Interference-free walks in time: Temporally disjoint paths (2022)
Journal Article
Klobas, N., Mertzios, G., Molter, H., Niedermeier, R., & Zschoche, P. (2022). Interference-free walks in time: Temporally disjoint paths. Autonomous Agents and Multi-Agent Systems, 37, Article 1. https://doi.org/10.1007/s10458-022-09583-5

We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically increasing tim... Read More about Interference-free walks in time: Temporally disjoint paths.

The complexity of quantified constraints: collapsibility, switchability and the algebraic formulation (2022)
Journal Article
Carvalho, C., Madelaine, F., Martin, B., & Zhuk, D. (2023). The complexity of quantified constraints: collapsibility, switchability and the algebraic formulation. ACM Transactions on Computational Logic, 24(1), Article 5. https://doi.org/10.1145/3568397

Let A be an idempotent algebra on a finite domain. By mediating between results of Chen [1] and Zhuk [2], we argue that if A satisfies the polynomially generated powers property (PGP) and B is a constraint language invariant under A (that is, in Inv(... Read More about The complexity of quantified constraints: collapsibility, switchability and the algebraic formulation.

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.

Equitable scheduling on a single machine (2022)
Journal Article
Heeger, K., Hermelin, D., Mertzios, G., Molter, H., Niedermeier, R., & Shabtay, D. (2023). Equitable scheduling on a single machine. Journal of Scheduling, 26(2), 209-225. https://doi.org/10.1007/s10951-022-00754-6

We introduce a natural but seemingly yet unstudied variant of the problem of scheduling jobs on a single machine so as to minimize the number of tardy jobs. The novelty of our new variant lies in simultaneously considering several instances of the pr... Read More about Equitable scheduling on a single machine.

Bent functions in the partial spread class generated by linear recurring sequences (2022)
Journal Article
Gadouleau, M., Mariot, L., & Picek, S. (2023). Bent functions in the partial spread class generated by linear recurring sequences. Designs, Codes and Cryptography, 91(1), 63-82. https://doi.org/10.1007/s10623-022-01097-1

We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if their feedba... Read More about Bent functions in the partial spread class generated by linear recurring sequences.

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.

On the Complexity of Optimising Variants of Phylogenetic Diversity on Phylogenetic Networks (2022)
Journal Article
Bordewich, M., Semple, C., & Wicke, K. (2022). On the Complexity of Optimising Variants of Phylogenetic Diversity on Phylogenetic Networks. Theoretical Computer Science, 917, 66-80. https://doi.org/10.1016/j.tcs.2022.03.012

Phylogenetic Diversity (PD) is a prominent quantitative measure of the biodiversity of a collection of present-day species (taxa). This measure is based on the evolutionary distance among the species in the collection. Loosely speaking, if T is a roo... Read More about On the Complexity of Optimising Variants of Phylogenetic Diversity on Phylogenetic Networks.

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.

On the Maximum Agreement Subtree Conjecture for Balanced Trees (2022)
Journal Article
Bordewich, M., Linz, S., Owen, M., St. John, K., Semple, C., & Wicke, K. (2022). On the Maximum Agreement Subtree Conjecture for Balanced Trees. SIAM Journal on Discrete Mathematics, 36(1), 336-354. https://doi.org/10.1137/20m1379678

We give a counterexample to the conjecture of Martin and Thatte that two balanced rooted binary leaf-labelled trees on n leaves have a maximum agreement subtree (MAST) of size at least n 1 2 . In particular, we show that for any c > 0, there exist tw... Read More about On the Maximum Agreement Subtree Conjecture for Balanced Trees.