Outputs (53)

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.

Disjoint paths and connected subgraphs for H-free graphs (2021)
Presentation / Conference Contribution
Kern, W., Martin, B., Paulusma, D., Smith, S., & van Leeuwen, E. Disjoint paths and connected subgraphs for H-free graphs

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 pairs. We determine, with an exception of two cases, the complexity of the Disjoint P... Read More about Disjoint paths and connected subgraphs for H-free graphs.

Injective colouring for H-free graphs (2021)
Presentation / Conference Contribution
Bok, J., Jedličková, N., Martin, B., Paulusma, D., & Smith, S. (2023, June). Injective colouring for H-free graphs. Presented at CSR 2021, Sochi

A function c : V (G) → {1, 2, . . . , k} is a k-colouring of a graph G if c(u) 6= c(v) whenever u and v are adjacent. If any two colour classes induce the disjoint union of vertices and edges, then c is called injective. Injective colourings are also... Read More about Injective colouring for H-free graphs.

Colouring graphs of bounded diameter in the absence of small cycles (2021)
Presentation / Conference Contribution
Martin, B., Paulusma, D., & Smith, S. (2021, May). Colouring graphs of bounded diameter in the absence of small cycles. Presented at CIAC 2021, Virtual Event

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 non-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... Read More about Colouring graphs of bounded diameter in the absence of small cycles.

Sherali-Adams and the binary encoding of combinatorial principles (2020)
Presentation / Conference Contribution
Dantchev, S., Ghani, A., & Martin, B. (2020, May). Sherali-Adams and the binary encoding of combinatorial principles. Presented at LATIN 2020, São Paulo, Brazil

We consider the Sherali-Adams ( SA ) refutation system together with the unusual binary encoding of certain combinatorial principles. For the unary encoding of the Pigeonhole Principle and the Least Number Principle, it is known that linear rank is r... Read More about Sherali-Adams and the binary encoding of combinatorial principles.

Acyclic, star and injective colouring: a complexity picture for H-free graphs (2020)
Presentation / Conference Contribution
Bok, J., Jedlickova, N., Martin, B., Paulusma, D., & Smith, S. (2020, September). Acyclic, star and injective colouring: a complexity picture for H-free graphs. Presented at ESA 2020, Pisa, Italy (Virtual Event)

A k-colouring c of a graph G is a mapping V(G) → {1,2,… k} such that c(u) ≠ c(v) whenever u and v are adjacent. The corresponding decision problem is Colouring. A colouring is acyclic, star, or injective if any two colour classes induce a forest, sta... Read More about Acyclic, star and injective colouring: a complexity picture for H-free graphs.

QCSP monsters and the demise of the chen conjecture (2020)
Presentation / Conference Contribution
Zhuk, D., & Martin, B. (2020, June). QCSP monsters and the demise of the chen conjecture. Presented at 52nd Annual ACM SIGACT Symposium on Theory of Computing, Chicago

We give a surprising classification for the computational complexity of the Quantified Constraint Satisfaction Problem over a constraint language Γ, QCSP(Γ), where Γ is a finite language over 3 elements which contains all constants. In particular, su... Read More about QCSP monsters and the demise of the chen conjecture.

Disconnected cuts in claw-free graphs (2020)
Journal Article
Martin, B., Paulusma, D., & van Leeuwen, E. (2020). Disconnected cuts in claw-free graphs. Journal of Computer and System Sciences, 113, 60-75. https://doi.org/10.1016/j.jcss.2020.04.005

A disconnected cut of a connected graph is a vertex cut that itself also induces a disconnected subgraph. The corresponding decision problem is called Disconnected Cut. This problem is known to be NP-hard on general graphs. We prove that it is polyno... Read More about Disconnected cuts in claw-free graphs.