Outputs (50)

Disjoint paths and connected subgraphs for H-free graphs (2021)
Conference Proceeding
Kern, W., Martin, B., Paulusma, D., Smith, S., & van Leeuwen, E. (2021). Disjoint paths and connected subgraphs for H-free graphs. In P. Flocchini, & L. Moura (Eds.), Combinatorial Algorithms: 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5–7, 2021, Proceedings (414-427). https://doi.org/10.1007/978-3-030-79987-8_29

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

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

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

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

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

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

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.

Colouring H-free graphs of bounded diameter (2019)
Presentation / Conference Contribution

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.

Resolution and the binary encoding of combinatorial principles (2019)
Presentation / Conference Contribution

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.

Constraint satisfaction problems for reducts of homogeneous graphs (2019)
Journal Article

For $n\geq 3$, let $(H_n, E)$ denote the $n$th Henson graph, i.e., the unique countable homogeneous graph with exactly those finite graphs as induced subgraphs that do not embed the complete graph on $n$ vertices. We show that for all structures $\Ga... Read More about Constraint satisfaction problems for reducts of homogeneous graphs.