Outputs (19)

Partitioning H-free graphs of bounded diameter (2021)
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.

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.

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.

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.