Outputs (314)

What graphs are 2-dot product graphs? (2021)
Journal Article
Johnson, M., Paulusma, D., & van Leeuwen, E. (2021). What graphs are 2-dot product graphs?. International Journal of Computational Geometry and Applications, 31(01), 1-16. https://doi.org/10.1142/s0218195921500011

Let d ≥ 1 be an integer. From a set of d-dimensional vectors, we obtain a d-dot product graph by letting each vector a u correspond to a vertex u and by adding an edge between two vertices u and v if and only if their dot product a u · a v ≥ t, for s... Read More about What graphs are 2-dot product graphs?.

Steiner Trees for Hereditary Graph Classes: a Treewidth Perspective (2021)
Journal Article
Bodlaender, H., Brettell, N., Johnson, M., Paesani, G., Paulusma, D., & van Leeuwen, E. (2021). Steiner Trees for Hereditary Graph Classes: a Treewidth Perspective. Theoretical Computer Science, 867, 30-39. https://doi.org/10.1016/j.tcs.2021.03.012

We consider the classical problems (Edge) Steiner Tree and Vertex Steiner Tree after restricting the input to some class of graphs characterized by a small set of forbidden induced subgraphs. We show a dichotomy for the former problem restricted to -... Read More about Steiner Trees for Hereditary Graph Classes: a Treewidth Perspective.

Bounding the mim-width of hereditary graph classes (2020)
Presentation / Conference Contribution
Brettell, N., Horsfield, J., Munaro, A., Paesani, G., & Paulusma, D. (2020, December). Bounding the mim-width of hereditary graph classes. Presented at IPEC 2020

A large number of NP-hard graph problems are solvable in XP time when parameterized by some width parameter. Hence, when solving problems on special graph classes, it is helpful to know if the graph class under consideration has bounded width. In thi... Read More about Bounding the mim-width of hereditary graph classes.

Contracting to a longest path in H-free graphs (2020)
Presentation / Conference Contribution
Kern, W., & Paulusma, D. (2020, December). Contracting to a longest path in H-free graphs. Presented at ISAAC 2020, Hong Kong, China

The Path Contraction problem has as input a graph G and an integer k and is to decide if G can be modified to the k-vertex path P_k by a sequence of edge contractions. A graph G is H-free for some graph H if G does not contain H as an induced subgrap... Read More about Contracting to a longest path in H-free graphs.

Steiner trees for hereditary graph classes (2020)
Presentation / Conference Contribution
Bodlaender, H., Brettell, N., Johnson, M., Paesani, G., Paulusma, D., & van Leeuwen, E. J. (2020, May). Steiner trees for hereditary graph classes. Presented at LATIN 2020, São Paulo

We consider the classical problems (Edge) Steiner Tree and Vertex Steiner Tree after restricting the input to some class of graphs characterized by a small set of forbidden induced subgraphs. We show a dichotomy for the former problem restricted to (... Read More about Steiner trees for hereditary graph classes.

Clique-Width: Harnessing the Power of Atoms (2020)
Presentation / Conference Contribution
Dabrowski, K. K., Masařík, T., Novotná, J., Paulusma, D., & Rzążewski, P. (2020, June). Clique-Width: Harnessing the Power of Atoms. Presented at WG 2020, Leeds, England

Many NP-complete graph problems are polynomial-time solvable on graph classes of bounded clique-width. Several of these problems are polynomial-time solvable on a hereditary graph class G if they are so on the atoms (graphs with no clique cut-set) of... Read More about Clique-Width: Harnessing the Power of Atoms.

Computing subset transversals in H-free graphs (2020)
Presentation / Conference Contribution
Brettell, N., Johnson, M., Paesani, G., & Paulusma, D. (2020, December). Computing subset transversals in H-free graphs. Presented at WG 2020, Leeds, England

We study the computational complexity of two well-known graph transversal problems, namely Subset Feedback Vertex Set and Subset Odd Cycle Transversal, by restricting the input to H-free graphs, that is, to graphs that do not contain some fixed graph... Read More about Computing subset transversals in H-free graphs.

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.

Graph isomorphism for (H1,H2)-free graphs: an almost complete dichotomy (2020)
Journal Article
Bonamy, M., Bousquet, N., Dabrowski, K., Johnson, M., Paulusma, D., & Pierron, T. (2021). Graph isomorphism for (H1,H2)-free graphs: an almost complete dichotomy. Algorithmica, 83(3), 822-852. https://doi.org/10.1007/s00453-020-00747-x

We resolve the computational complexity of GRAPH ISOMORPHISM for classes of graphs characterized by two forbidden induced subgraphs H_{1} and H_2 for all but six pairs (H_1,H_2). Schweitzer had previously shown that the number of open cases was finit... Read More about Graph isomorphism for (H1,H2)-free graphs: an almost complete dichotomy.

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.