Skip to main content

Research Repository

Advanced Search

All Outputs (25)

Edge Multiway Cut and Node Multiway Cut are hard for planar subcubic graphs (2024)
Presentation / Conference Contribution
Johnson, M., Martin, B., Pandey, S., Paulusma, D., Smith, S., & van Leeuwen, E. J. (2024, June). Edge Multiway Cut and Node Multiway Cut are hard for planar subcubic graphs. Presented at SWAT 2024, Helsinki, Finland

It is known that the weighted version of Edge Multiway Cut (also known as Multiterminal Cut) is NP-complete on planar graphs of maximum degree 3. In contrast, for the unweighted version, NP-completeness is only known for planar graphs of maximum degr... Read More about Edge Multiway Cut and Node Multiway Cut are hard for planar subcubic graphs.

Complexity Framework for Forbidden Subgraphs III: When Problems are Tractable on Subcubic Graphs (2023)
Presentation / Conference Contribution
Johnson, M., Martin, B., Pandey, S., Paulusma, D., Smith, S., & Van Leeuwen, E. J. (2023, August). Complexity Framework for Forbidden Subgraphs III: When Problems are Tractable on Subcubic Graphs. Presented at 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023), Bordeaux, France

For any finite set H = {H1,. .. , Hp} of graphs, a graph is H-subgraph-free if it does not contain any of H1,. .. , Hp as a subgraph. In recent work, meta-classifications have been studied: these show that if graph problems satisfy certain prescribed... Read More about Complexity Framework for Forbidden Subgraphs III: When Problems are Tractable on Subcubic Graphs.

Computing weighted subset transversals in H-free graphs (2021)
Presentation / Conference Contribution
Brettell, N., Johnson, M., & Paulusma, D. (2021, August). Computing weighted subset transversals in H-free graphs. Presented at WADS 2021, Halifax, Nova Scotia

For the Odd Cycle Transversal problem, the task is to nd a small set S of vertices in a graph that intersects every cycle of odd length. The Subset Odd Cycle Transversal requires S to intersect only those odd cycles that include a vertex of a disting... Read More about Computing weighted subset transversals 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.

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.

Independent transversals versus transversals (2019)
Presentation / Conference Contribution
Dabrowski, K., Johnson, M., Paesani, G., Paulusma, D., & Zamaraev, V. (2019, December). Independent transversals versus transversals. Presented at EuroComb 2019, Bratislava, Slovakia

We compare the minimum size of a vertex cover, feedback vertex set and odd cycle transversal of a graph with the minimum size of the corresponding variants in which the transversal must be an independent set. We investigate for which graphs H the two... Read More about Independent transversals versus transversals.

On cycle transversals and their connected variants in the absence of a small linear forest (2019)
Presentation / Conference Contribution
Feghali, C., Johnson, M., Paesani, G., & Paulusma, D. (2019, August). On cycle transversals and their connected variants in the absence of a small linear forest. Presented at FCT 2019, Copenhagen, Denmark

A graph is H-free if it contains no induced subgraph isomorphic to H. We prove new complexity results for the two classical cycle transversal problems Feedback Vertex Set and Odd Cycle Transversal by showing that they can be solved in polynomial time... Read More about On cycle transversals and their connected variants in the absence of a small linear forest.

Graph isomorphism for (H1,H2)-free graphs: an almost complete dichotomy (2019)
Presentation / Conference Contribution
Bonamy, M., Dabrowski, K. K., Johnson, M., & Paulusma, D. (2019, December). Graph isomorphism for (H1,H2)-free graphs: an almost complete dichotomy. Presented at WADS 2019, Edmonton, Canada

We almost completely resolve the computational complexity of Graph Isomorphism for classes of graphs characterized by two forbidden induced subgraphs H1 and H2. Schweitzer settled the complexity of this problem restricted to (H1;H2)-free graphs for a... Read More about Graph isomorphism for (H1,H2)-free graphs: an almost complete dichotomy.

Finding a small number of colourful components (2019)
Presentation / Conference Contribution
Bulteau, L., Dabrowski, K., Fertin, G., Johnson, M., Paulusma, D., & Vialette, S. (2019, December). Finding a small number of colourful components. Presented at CPM 2019, Pisa, Italy

Connected Vertex Cover for (sP1+P5)-free graphs (2018)
Presentation / Conference Contribution
Johnson, M., Paesani, G., & Paulusma, D. (2018, June). Connected Vertex Cover for (sP1+P5)-free graphs. Presented at 44th International Workshop on Graph-Theoretic Concepts in Computer Science (WG 2018)., Cottbus, Germany

The Connected Vertex Cover problem is to decide if a graph G has a vertex cover of size at most k that induces a connected subgraph of G. This is a well-studied problem, known to be NP-complete for restricted graph classes, and, in particular, for H-... Read More about Connected Vertex Cover for (sP1+P5)-free graphs.

On the price of independence for vertex cover, feedback vertex set and odd cycle transversal (2018)
Presentation / Conference Contribution
Dabrowski, K. K., Johnson, M., Paesani, G., Paulusma, D., & Zamaraev, V. (2018, August). On the price of independence for vertex cover, feedback vertex set and odd cycle transversal. Presented at 43nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)., Liverpool, UK

Let vc(G), fvs(G) and oct(G) denote, respectively, the size of a minimum vertex cover, minimum feedback vertex set and minimum odd cycle transversal in a graph G. One can ask, when looking for these sets in a graph, how much bigger might they be if w... Read More about On the price of independence for vertex cover, feedback vertex set and odd cycle transversal.

Clique-Width for Graph Classes Closed under Complementation (2017)
Presentation / Conference Contribution
Blanché, A., Dabrowski, K. K., Johnson, M., Lozin, V. V., Paulusma, D., & Zamaraev, V. (2017, August). Clique-Width for Graph Classes Closed under Complementation. Presented at 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS)., Aalborg, Denmark

Clique-width is an important graph parameter due to its algorithmic and structural properties. A graph class is hereditary if it can be characterized by a (not necessarily finite) set H of forbidden induced subgraphs. We initiate a systematic study i... Read More about Clique-Width for Graph Classes Closed under Complementation.

Recognizing Graphs Close to Bipartite Graphs (2017)
Presentation / Conference Contribution
Bonamy, M., Dabrowski, K. K., Feghali, C., Johnson, M., & Paulusma, D. (2017, August). Recognizing Graphs Close to Bipartite Graphs. Presented at 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS)., Aalborg, Denmark

We continue research into a well-studied family of problems that ask if the vertices of a graph can be partitioned into sets A and B, where A is an independent set and B induces a graph from some specified graph class G. We let G be the class of k-de... Read More about Recognizing Graphs Close to Bipartite Graphs.

Surjective H-Colouring: new hardness results (2017)
Presentation / Conference Contribution
Golovach, P. A., Johnson, M., Martin, M., Paulusma, D., & Stewart, A. (2017, June). Surjective H-Colouring: new hardness results. Presented at Computability in Europe (CiE 2017)., Turku, Finland

A homomorphism from a graph G to a graph H is a vertex mapping f from the vertex set of G to the vertex set of H such that there is an edge between vertices f(u) and f(v) of H whenever there is an edge between vertices u and v of G. The H-Colouring p... Read More about Surjective H-Colouring: new hardness results.

Independent Feedback Vertex Set for P5-free Graphs (2017)
Presentation / Conference Contribution
Bonamy, M., Dabrowski, K. K., Feghali, C., Johnson, M., & Paulusma, D. (2017, December). Independent Feedback Vertex Set for P5-free Graphs. Presented at ISAAC 2017

The NP-complete problem Feedback Vertex Set is to decide if it is possible, for a given integer k ≥ 0, to delete at most k vertices from a given graph so that what remains is a forest. The variant in which the deleted vertices must form an independen... Read More about Independent Feedback Vertex Set for P5-free Graphs.

Filling the complexity gaps for colouring planar and bounded degree graphs (2016)
Presentation / Conference Contribution
Dabrowski, K. K., Dross, F., Johnson, M., & Paulusma, D. (2015, October). Filling the complexity gaps for colouring planar and bounded degree graphs. Presented at 26th International Workshop on Combinatorial Algorithms (IWOCA 2015), Verona, Italy

We consider a natural restriction of the List Colouring problem, k-Regular List Colouring, which corresponds to the List Colouring problem where every list has size exactly k. We give a complete classification of the complexity of k-Regular List Colo... Read More about Filling the complexity gaps for colouring planar and bounded degree graphs.

Kempe equivalence of colourings of cubic graphs (2015)
Presentation / Conference Contribution
Feghali, C., Johnson, M., & Paulusma, D. (2015, November). Kempe equivalence of colourings of cubic graphs. Presented at European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2015),, Bergen, Norway

Given a graph G = (V,E) and a proper vertex colouring of G, a Kempe chain is a subset of V that induces a maximal connected subgraph of G in which every vertex has one of two colours. To make a Kempe change is to obtain one colouring from another by... Read More about Kempe equivalence of colourings of cubic graphs.

What graphs are 2-dot product graphs? (2015)
Presentation / Conference Contribution
Johnson, M., van Leeuwen, E., & Paulusma, D. (2015, November). What graphs are 2-dot product graphs?. Presented at European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2015),, Bergen, Norway

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