All Outputs (6)

Hereditary graph classes: when the complexities of coloring and clique cover coincide (2018)
Journal Article
Blanché, A., Dabrowski, K., Johnson, M., & Paulusma, D. (2019). Hereditary graph classes: when the complexities of coloring and clique cover coincide. Journal of Graph Theory, 91(3), 267-289. https://doi.org/10.1002/jgt.22431

graph is (H1;H2)-free for a pair of graphs H1;H2 if it contains no induced subgraph isomorphic to H1 or H2. In 2001, Král’, Kratochvíl, Tuza, and Woeginger initiated a study into the complexity of Colouring for (H1;H2)-free graphs. Since then, others... Read More about Hereditary graph classes: when the complexities of coloring and clique cover coincide.

Computing small pivot-minors (2018)
Conference Proceeding
Dabrowski, K. K., Dross, F., Jeong, J., Kanté, M. M., Kwon, O., Oum, S., & Paulusma, D. (2018). Computing small pivot-minors. In A. Brandstädt, E. Köhler, & K. Meer (Eds.), Graph-Theoretic Concepts in Computer Science, 44th International Workshop, WG 2018, Cottbus, Germany, June 27–29, 2018 ; proceedings (125-138). https://doi.org/10.1007/978-3-030-00256-5_11

A graph G contains a graph H as a pivot-minor if H can be obtained from G by applying a sequence of vertex deletions and edge pivots. Pivot-minors play an important role in the study of rank-width. However, so far, pivot-minors have only been studied... Read More about Computing small pivot-minors.

On the (Parameterized) Complexity of Recognizing Well-covered ( r , ℓ )-graph (2018)
Journal Article
Alves, S. R., Dabrowski, K. K., Faria, L., Klein, S., Sau, I., & Souza, U. S. (2018). On the (Parameterized) Complexity of Recognizing Well-covered ( r , ℓ )-graph. Theoretical Computer Science, 746, 36-48. https://doi.org/10.1016/j.tcs.2018.06.024

An (r,ℓ)(r,ℓ)-partition of a graph G is a partition of its vertex set into r independent sets and ℓ cliques. A graph is (r,ℓ)(r,ℓ) if it admits an (r,ℓ)(r,ℓ)-partition. A graph is well-covered if every maximal independent set is also maximum. A graph... Read More about On the (Parameterized) Complexity of Recognizing Well-covered ( r , ℓ )-graph.

Independent Feedback Vertex Set for P5-free Graphs (2018)
Journal Article
Bonamy, M., Dabrowski, K., Feghali, C., Johnson, M., & Paulusma, D. (2018). Independent Feedback Vertex Set for P5-free Graphs. Algorithmica, 81(4), 1416-1449. https://doi.org/10.1007/s00453-018-0474-x

The NP-complete problem Feedback Vertex Set is that of deciding whether or not 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... Read More about Independent Feedback Vertex Set for P5-free Graphs.

On colouring (2P2,H)-free and (P5,H)-free graphs (2018)
Journal Article
Dabrowski, K., & Paulusma, D. (2018). On colouring (2P2,H)-free and (P5,H)-free graphs. Information Processing Letters, 134, 35-41. https://doi.org/10.1016/j.ipl.2018.02.003

The Colouring problem asks whether the vertices of a graph can be coloured with at most k colours for a given integer k in such a way that no two adjacent vertices receive the same colour. A graph is (H1,H2)-free if it has no induced subgraph isomorp... Read More about On colouring (2P2,H)-free and (P5,H)-free graphs.

On the price of independence for vertex cover, feedback vertex set and odd cycle transversal (2018)
Conference Proceeding
Dabrowski, K. K., Johnson, M., Paesani, G., Paulusma, D., & Zamaraev, V. (2018). On the price of independence for vertex cover, feedback vertex set and odd cycle transversal. In I. Potapov, P. Spirakis, & J. Worrell (Eds.), 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018) (63:1-63:15). https://doi.org/10.4230/lipics.mfcs.2018.63

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.