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Outputs (17)

Simple games versus weighted voting games: bounding the critical threshold value (2019)
Journal Article
Hof, F., Kern, W., Kurz, S., Pashkovich, K., & Paulusma, D. (2020). Simple games versus weighted voting games: bounding the critical threshold value. Social Choice and Welfare, 54(4), 609-621. https://doi.org/10.1007/s00355-019-01221-6

A simple game (N; v) is given by a set N of n players and a partition of 2N into a set L of losing coalitions L with value v(L) = 0 that is closed under taking subsets and a set W of winning coalitions W with value v(W) = 1. We let = minp>0;p6=0 maxW... Read More about Simple games versus weighted voting games: bounding the critical threshold value.

Clique-width and well-quasi ordering of triangle-free graph classes (2019)
Journal Article
Dabrowski, K., Lozin, V., & Paulusma, D. (2020). Clique-width and well-quasi ordering of triangle-free graph classes. Journal of Computer and System Sciences, 108, 64-91. https://doi.org/10.1016/j.jcss.2019.09.001

We obtain a complete classification of graphs H for which the class of -free graphs is well-quasi-ordered by the induced subgraph relation and an almost complete classification of graphs H for which the class of -free graphs has bounded clique-width.... Read More about Clique-width and well-quasi ordering of triangle-free graph classes.

Colouring H-free graphs of bounded diameter (2019)
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.

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.

Tree pivot-minors and linear rank-width (2019)
Presentation / Conference Contribution
Dabrowski, K., Dross, F., Jeong, J., Kanté, M., Kwon, O., Oum, S., & Paulusma, D. (2019, July). Tree pivot-minors and linear rank-width. Presented at EuroComb 2019, Bratislava, Slovakia

Treewidth and its linear variant path-width play a central role for the graph minor relation. Rank-width and linear rank-width do the same for the graph pivot-minor relation. Robertson and Seymour (1983) proved that for every tree T there exists a co... Read More about Tree pivot-minors and linear rank-width.

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.

Clique-width for hereditary graph classes (2019)
Journal Article
Dabrowski, K., Johnson, M., & Paulusma, D. (online). Clique-width for hereditary graph classes. https://doi.org/10.1017/9781108649094.002

Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class G is bounded by a constant, a wide range of problems that are NP-complete in general can be shown to be po... Read More about Clique-width for hereditary graph classes.

Colouring Square-Free Graphs without Long Induced Paths (2019)
Journal Article
Gaspers, S., Huang, S., & Paulusma, D. (2019). Colouring Square-Free Graphs without Long Induced Paths. Journal of Computer and System Sciences, 106, 60-79. https://doi.org/10.1016/j.jcss.2019.06.002

The complexity of Colouring is fully understood for H-free graphs, but there are still major complexity gaps if two induced subgraphs and are forbidden. Let be the s-vertex cycle and be the t-vertex path . We show that Colouring is polynomial-time so... Read More about Colouring Square-Free Graphs without Long Induced Paths.

Connected vertex cover for (sP1+P5)-free graphs (2019)
Journal Article
Johnson, M., Paesani, G., & Paulusma, D. (2020). Connected vertex cover for (sP1+P5)-free graphs. Algorithmica, 82(1), 20-40. https://doi.org/10.1007/s00453-019-00601-9

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.

Using contracted solution graphs for solving reconfiguration problems (2019)
Journal Article
Bonsma, P., & Paulusma, D. (2019). Using contracted solution graphs for solving reconfiguration problems. Acta Informatica, 56(7-8), 619-648. https://doi.org/10.1007/s00236-019-00336-8

We introduce in a general setting a dynamic programming method for solving reconfiguration problems. Our method is based on contracted solution graphs, which are obtained from solution graphs by performing an appropriate series of edge contractions t... Read More about Using contracted solution graphs for solving reconfiguration problems.

Filling the complexity gaps for colouring planar and bounded degree graphs (2019)
Journal Article
Dabrowski, K., Dross, F., Johnson, M., & Paulusma, D. (2019). Filling the complexity gaps for colouring planar and bounded degree graphs. Journal of Graph Theory, 92(4), 377-393. https://doi.org/10.1002/jgt.22459

A colouring of a graphGVE=( ,)is a function→cV:{1, 2,...}such that≠cucv() ()for every∈uvE.Ak‐regular list assignment ofGis a functionLwith domainVsuch that for every∈uV,Lu()is asubset of{1, 2,...}of sizek. A colouringcofGrespects ak‐regular list assi... Read More about Filling the complexity gaps for colouring planar and bounded degree graphs.

Algorithms for outerplanar graph roots and graph roots of pathwidth at most 2 (2019)
Journal Article
Golovach, P., Heggernes, P., Kratch, D., Lima, P., & Paulusma, D. (2019). Algorithms for outerplanar graph roots and graph roots of pathwidth at most 2. Algorithmica, 81(7), 2795-2828. https://doi.org/10.1007/s00453-019-00555-y

Deciding if a graph has a square root is a classical problem, which has been studied extensively both from graph-theoretic and algorithmic perspective. As the problem is NP-complete, substantial effort has been dedicated to determining the complexity... Read More about Algorithms for outerplanar graph roots and graph roots of pathwidth at most 2.

Classifying k-Edge Colouring for H-free Graphs (2019)
Journal Article
Galby, E., Lima, P., Paulusma, D., & Ries, B. (2019). Classifying k-Edge Colouring for H-free Graphs. Information Processing Letters, 146, 39-43. https://doi.org/10.1016/j.ipl.2019.02.006

A graph is H-free if it does not contain an induced subgraph isomorphic to H. For every integer k and every graph H, we determine the computational complexity of k-Edge Colouring for H-free graphs.

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