All Outputs (53)

Classification Transfer for Qualitative Reasoning Problems
Presentation / Conference Contribution
Bodirsky, M., Jonsson, P., Martin, B., & Mottet, A. (2018, July). Classification Transfer for Qualitative Reasoning Problems. Presented at IJCAI-ECAI 2018, the 27th International Joint Conference on Artificial Intelligence and the 23rd European Conference on Artificial Intelligence., Stockholm, Sweden

We study formalisms for temporal and spatial reasoning in the modern context of Constraint Satisfaction Problems (CSPs). We show how questions on the complexity of their subclasses can be solved using existing results via the powerful use of primitiv... Read More about Classification Transfer for Qualitative Reasoning Problems.

Disconnected Cuts in Claw-free Graphs
Presentation / Conference Contribution
Martin, B., Paulusma, D., & van Leeuwen, E. J. (2018, August). Disconnected Cuts in Claw-free Graphs. Presented at 26th Annual European Symposium on Algorithms (ESA 2018)., Helsinki, Finland

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. It is known that Disconnected Cut is NP-hard on general graphs, while polynomial-... Read More about Disconnected Cuts in Claw-free Graphs.

Colouring H-free graphs of bounded diameter
Presentation / Conference Contribution
Martin, B., Paulusma, D., & Smith, S. (2019, August). Colouring H-free graphs of bounded diameter. Presented at MFCS 2019, Aachen, Germany

The 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 induced subgraph. It is kn... Read More about Colouring H-free graphs of bounded diameter.

Acyclic, star and injective colouring: a complexity picture for H-free graphs
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.

Resolution and the binary encoding of combinatorial principles
Presentation / Conference Contribution
Dantchev, S., Galesi, N., & Martin, B. (2019, July). Resolution and the binary encoding of combinatorial principles. Presented at Computational Complexity Conference, New Brunswick, New Jersey, USA

Res(s) is an extension of Resolution working on s-DNFs. We prove tight n (k) lower bounds for the size of refutations of the binary version of the k-Clique Principle in Res(o(log log n)). Our result improves that of Lauria, Pudlák et al. [27] who pro... Read More about Resolution and the binary encoding of combinatorial principles.

QCSP monsters and the demise of the chen conjecture
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.

Sherali-Adams and the binary encoding of combinatorial principles
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.

Colouring graphs of bounded diameter in the absence of small cycles
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.

Injective colouring for H-free graphs
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.

QCSP on reflexive tournaments
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.

Partitioning H-free graphs of bounded diameter
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.

The Complexity of L(p,q)-Edge-Labelling
Presentation / Conference Contribution
Berthe, G., Martin, B., Paulusma, D., & Smith, S. (2022, March). The Complexity of L(p,q)-Edge-Labelling. Presented at The 15th International Conference and Workshops on Algorithms and Computation (WALCOM 2021), University of Jember, East Java

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.

Few induced disjoint paths for H-free graphs
Presentation / Conference Contribution
Martin, B., Paulusma, D., Smith, S., & van Leeuwen, E. (2022, May). Few induced disjoint paths for H-free graphs. Presented at ISCO 2022, Online

Paths P 1 , . . . , P k in a graph G = (V, E) are mutually induced if any two distinct P i and P j 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... Read More about Few induced disjoint paths for H-free graphs.