Professor Daniel Paulusma's Outputs (21)

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?.

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.

Bounding the clique-width of H-free split graphs (2015)
Presentation / Conference Contribution
Brandstädt, A., Dabrowski, K., Huang, S., & Paulusma, D. (2015, November). Bounding the clique-width of H-free split graphs. Presented at European Conference on Combinatorics, Graph Theory and Applications (EuroComb 2015),, Bergen, Norway

A graph is H-free if it has no induced subgraph isomorphic to H. We continue a study into the boundedness of clique-width of subclasses of perfect graphs. We identify five new classes of H-free split graphs whose clique-width is bounded. Our main res... Read More about Bounding the clique-width of H-free split graphs.

Editing to Eulerian graphs (2015)
Journal Article
Dabrowski, K., Golovach, P., van 't Hof, P., & Paulusma, D. (2016). Editing to Eulerian graphs. Journal of Computer and System Sciences, 82(2), 213-228. https://doi.org/10.1016/j.jcss.2015.10.003

The Eulerian Editing problem asks, given a graph G and an integer k, whether G can be modified into an Eulerian graph using at most k edge additions and edge deletions. We show that this problem is polynomial-time solvable for both undirected and dir... Read More about Editing to Eulerian graphs.

Narrowing the complexity gap for colouring (Cs, Pt)-free graphs (2015)
Journal Article
Huang, S., Johnson, M., & Paulusma, D. (2015). Narrowing the complexity gap for colouring (Cs, Pt)-free graphs. The Computer Journal, 58(11), 3074-3088. https://doi.org/10.1093/comjnl/bxv039

For a positive integer k and graph G=(V,E), a k-colouring of G is a mapping c:V→{1,2,…,k} such that c(u)≠c(v) whenever uv∈E. The k-Colouring problem is to decide, for a given G, whether a k-colouring of G exists. The k-Precolouring Extension problem... Read More about Narrowing the complexity gap for colouring (Cs, Pt)-free graphs.

A Reconfigurations Analogue of Brooks' Theorem and Its Consequences (2015)
Journal Article
Feghali, C., Johnson, M., & Paulusma, D. (2016). A Reconfigurations Analogue of Brooks' Theorem and Its Consequences. Journal of Graph Theory, 83(4), 340-358. https://doi.org/10.1002/jgt.22000

Let G be a simple undirected connected graph on n vertices with maximum degree Δ. Brooks' Theorem states that G has a proper Δ-coloring unless G is a complete graph, or a cycle with an odd number of vertices. To recolor G is to obtain a new proper co... Read More about A Reconfigurations Analogue of Brooks' Theorem and Its Consequences.

Knocking out P_k-free graphs (2015)
Journal Article
Johnson, M., Paulusma, D., & Stewart, A. (2015). Knocking out P_k-free graphs. Discrete Applied Mathematics, 190-191, 100-108. https://doi.org/10.1016/j.dam.2015.04.010

A parallel knock-out scheme for a graph proceeds in rounds in each of which each surviving vertex eliminates one of its surviving neighbours. A graph is KO-reducible if there exists such a scheme that eliminates every vertex in the graph. The Paralle... Read More about Knocking out P_k-free graphs.

Bounding the Clique-Width of H-free Chordal Graphs (2015)
Presentation / Conference Contribution
Brandstädt, A., Dabrowski, K., Huang, S., & Paulusma, D. (2015, August). Bounding the Clique-Width of H-free Chordal Graphs. Presented at 40th International Symposium, MFCS 2015, Milan, Italy

A graph is H-free if it has no induced subgraph isomorphic to H. Brandstädt, Engelfriet, Le and Lozin proved that the class of chordal graphs with independence number at most 3 has unbounded clique-width. Brandstädt, Le and Mosca erroneously claimed... Read More about Bounding the Clique-Width of H-free Chordal Graphs.

The price of connectivity for cycle transversals (2015)
Presentation / Conference Contribution
Hartinger, T., Johnson, M., Milanič, M., & Paulusma, D. (2015, August). The price of connectivity for cycle transversals. Presented at 40th International Symposium, MFCS 2015, Milan, Italy

For a family of graphs F, an F-transversal of a graph G is a subset S⊆V(G) that intersects every subset of V(G) that induces a subgraph isomorphic to a graph in F. Let tF(G) be the minimum size of an F-transversal of G, and ctF(G) be the minimum size... Read More about The price of connectivity for cycle transversals.

Minimal disconnected cuts in planar graphs (2015)
Presentation / Conference Contribution
Kamiński, M., Paulusma, D., Stewart, A., & Thilikos, D. M. (2015, August). Minimal disconnected cuts in planar graphs. Presented at 20th International Symposium, FCT 2015, Gdańsk, Poland

The problem of finding a disconnected cut in a graph is NP-hard in general but polynomial-time solvable on planar graphs. The problem of finding a minimal disconnected cut is also NP-hard but its computational complexity is not known for planar graph... Read More about Minimal disconnected cuts in planar graphs.

Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree (2015)
Journal Article
Chaplick, S., Fiala, J., Hof, V. '. P., Paulusma, D., & Tesař, M. (2015). Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree. Theoretical Computer Science, 590, 86-95. https://doi.org/10.1016/j.tcs.2015.01.028

A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of testing whether... Read More about Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree.

Model counting for CNF formulas of bounded modular treewidth (2015)
Journal Article
Paulusma, D., Slivovsky, S., & Szeider, S. (2016). Model counting for CNF formulas of bounded modular treewidth. Algorithmica, 76(1), 168-194. https://doi.org/10.1007/s00453-015-0030-x

We define the modular treewidth of a graph as its treewidth after contraction of modules. This parameter properly generalizes treewidth and is itself properly generalized by clique-width. We show that the number of satisfying assignments can be compu... Read More about Model counting for CNF formulas of bounded modular treewidth.

Classifying the clique-width of H-free bipartite graphs (2015)
Journal Article
Dabrowski, K., & Paulusma, D. (2016). Classifying the clique-width of H-free bipartite graphs. Discrete Applied Mathematics, 200, 43-51. https://doi.org/10.1016/j.dam.2015.06.030

Let GG be a bipartite graph, and let HH be a bipartite graph with a fixed bipartition (BH,WH)(BH,WH). We consider three different, natural ways of forbidding HH as an induced subgraph in GG. First, GG is HH-free if it does not contain HH as an induce... Read More about Classifying the clique-width of H-free bipartite graphs.

Editing to a planar graph of given degrees (2015)
Presentation / Conference Contribution
Dabrowski, K., Golovach, P., van 't Hof, P., Paulusma, D., & Thilikos, D. (2015, June). Editing to a planar graph of given degrees

We consider the following graph modification problem. Let the input consist of a graph G=(V,E), a weight function w:V∪E→N, a cost function c:V∪E→N and a degree function δ:V→N0, together with three integers kv, ke and C. The question is whether we can... Read More about Editing to a planar graph of given degrees.

Contraction blockers for graphs with forbidden induced paths (2015)
Presentation / Conference Contribution
Diner, Ö., Paulusma, D., Picouleau, C., & Ries, B. (2015, March). Contraction blockers for graphs with forbidden induced paths. Presented at 9th International Conference on Algorithms and Complexity (CIAC 2015), Paris, France

We consider the following problem: can a certain graph parameter of some given graph be reduced by at least d for some integer d via at most k edge contractions for some given integer k? We examine three graph parameters: the chromatic number, clique... Read More about Contraction blockers for graphs with forbidden induced paths.

Clique-width of graph classes defined by two forbidden induced subgraphs (2015)
Presentation / Conference Contribution
Dabrowski, K. K., & Paulusma, D. (2015, March). Clique-width of graph classes defined by two forbidden induced subgraphs. Presented at 9th International Conference on Algorithms and Complexity (CIAC 2015), Paris, France

If a graph has no induced subgraph isomorphic to any graph in a finite family {H1,…,Hp}, it is said to be (H1,…,Hp)-free. The class of H-free graphs has bounded clique-width if and only if H is an induced subgraph of the 4-vertex path P4. We study th... Read More about Clique-width of graph classes defined by two forbidden induced subgraphs.

Finding Shortest Paths Between Graph Colourings (2015)
Journal Article
Johnson, M., Kratsch, D., Kratsch, S., Patel, V., & Paulusma, D. (2016). Finding Shortest Paths Between Graph Colourings. Algorithmica, 75(2), 295-321. https://doi.org/10.1007/s00453-015-0009-7

The k-colouring reconguration problem asks whether, for a given graph G, two proper k-colourings and of G, and a positive integer `, there exists a sequence of at most ` + 1 proper k-colourings of G which starts with and ends with and where successiv... Read More about Finding Shortest Paths Between Graph Colourings.

Algorithms for diversity and clustering in social networks through dot product graphs (2015)
Journal Article
Johnson, M., Paulusma, D., & van Leeuwen, E. (2015). Algorithms for diversity and clustering in social networks through dot product graphs. Social Networks, 41, 48-55. https://doi.org/10.1016/j.socnet.2015.01.001

In this paper, we investigate a graph-theoretical model of social networks. The dot product model assumes that two individuals are connected in the social network if their attributes or opinions are similar. In the model, a d -dimensional vector View... Read More about Algorithms for diversity and clustering in social networks through dot product graphs.

Bounding clique-width via perfect graphs (2015)
Presentation / Conference Contribution
Dabrowski, K. K., Huang, S., & Paulusma, D. (2015, March). Bounding clique-width via perfect graphs. Presented at International Conference on Language and Automata Theory and Applications, Nice, France

Given two graphs H1 and H2, a graph G is (H1,H2)-free if it contains no subgraph isomorphic to H1 or H2. We continue a recent study into the clique-width of (H1,H2)-free graphs and present three new classes of (H1,H2)-free graphs that have bounded cl... Read More about Bounding clique-width via perfect graphs.

Induced disjoint paths in claw-free graphs (2015)
Journal Article
Golovach, P., Paulusma, D., & van Leeuwen, E. (2015). Induced disjoint paths in claw-free graphs. SIAM Journal on Discrete Mathematics, 29(1), 348-375. https://doi.org/10.1137/140963200

Paths P1; : : : ; Pk in a graph G = (V;E) are said to be mutually induced if for any 1 i < j k, Pi and Pj have neither common vertices nor adjacent vertices (except perhaps their end-vertices). The Induced Disjoint Paths problem is to test whether a... Read More about Induced disjoint paths in claw-free graphs.