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Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration (2021)
Journal Article
Bonamy, M., Dabrowski, K., Feghali, C., Johnson, M., & Paulusma, D. (2021). Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration. Journal of Graph Theory, 98(1), 81-109. https://doi.org/10.1002/jgt.22683

We continue research into a well-studied family of problems that ask whether the vertices of a given 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 consider the ca... Read More about Recognizing Graphs Close to Bipartite Graphs with an Application to Colouring Reconfiguration.

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.

Clique-width for graph classes closed under complementation (2020)
Journal Article
Blanché, A., Dabrowski, K., Johnson, M., Lozin, V., Paulusma, D., & Zamaraev, V. (2020). Clique-width for graph classes closed under complementation. SIAM Journal on Discrete Mathematics, 34(2), 1107-1147. https://doi.org/10.1137/18m1235016

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 study the boundedness of cliq... Read More about Clique-width for graph classes closed under complementation.

On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear Forest (2020)
Journal Article
Dabrowski, K., Feghali, C., Johnson, M., Paesani, G., Paulusma, D., & Rzążewski, P. (2020). On Cycle Transversals and Their Connected Variants in the Absence of a Small Linear Forest. Algorithmica, 82(10), 2841-2866. https://doi.org/10.1007/s00453-020-00706-6

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 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.

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.

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.

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.

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.

Independent feedback vertex sets for graphs of bounded diameter (2017)
Journal Article
Bonamy, M., Dabrowski, K., Feghali, C., Johnson, M., & Paulusma, D. (2018). Independent feedback vertex sets for graphs of bounded diameter. Information Processing Letters, 131, 26-32. https://doi.org/10.1016/j.ipl.2017.11.004

The Near-Bipartiteness problem is that of deciding whether or not the vertices of a graph can be partitioned into sets A and B, where A is an independent set and B induces a forest. The set A in such a partition is said to be an independent feedback... Read More about Independent feedback vertex sets for graphs of bounded diameter.

Contracting Bipartite Graphs to Paths and Cycles (2017)
Journal Article
Dabrowski, K., & Paulusma, D. (2017). Contracting Bipartite Graphs to Paths and Cycles. Information Processing Letters, 127, 37-42. https://doi.org/10.1016/j.ipl.2017.06.013

Testing if a given graph G contains the k -vertex path Pk as a minor or as an induced minor is trivial for every fixed integer k≥1. However, the situation changes for the problem of checking if a graph can be modified into Pk by using only edge contr... Read More about Contracting Bipartite Graphs to Paths and Cycles.

Well-quasi-ordering versus clique-width: new results on bigenic classes (2017)
Journal Article
Dabrowski, K., Lozin, V., & Paulusma, D. (2018). Well-quasi-ordering versus clique-width: new results on bigenic classes. Order, 35(2), 253-274. https://doi.org/10.1007/s11083-017-9430-7

Daligault, Rao and Thomassé asked whether a hereditary class of graphs well-quasi-ordered by the induced subgraph relation has bounded clique-width. Lozin, Razgon and Zamaraev recently showed that this is not true for classes defined by infinitely ma... Read More about Well-quasi-ordering versus clique-width: new results on bigenic classes.

Colouring Diamond-free Graphs (2017)
Journal Article
Dabrowski, K., Dross, F., & Paulusma, D. (2017). Colouring Diamond-free Graphs. Journal of Computer and System Sciences, 89, 410-431. https://doi.org/10.1016/j.jcss.2017.06.005

The Colouring problem is that of deciding, given a graph G and an integer k, whether G admits a (proper) k-colouring. For all graphs H up to five vertices, we classify the computational complexity of Colouring for (diamond,H)-free graphs. Our proof i... Read More about Colouring Diamond-free Graphs.

Bounding the Clique-Width of H-free Chordal Graphs (2017)
Journal Article
Brandstädt, A., Dabrowski, K., Huang, S., & Paulusma, D. (2017). Bounding the Clique-Width of H-free Chordal Graphs. Journal of Graph Theory, 86(1), 42-77. https://doi.org/10.1002/jgt.22111

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 claime... Read More about Bounding the Clique-Width of H-free Chordal Graphs.

Editing to a Planar Graph of Given Degrees (2016)
Journal Article
Dabrowski, K., Golovach, P., van 't Hof, P., Paulusma, D., & Thilikos, D. (2016). Editing to a Planar Graph of Given Degrees. Journal of Computer and System Sciences, 85, 168-182. https://doi.org/10.1016/j.jcss.2016.11.009

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→N0 and a degree function δ:V→N0, together with three integers kv,ke and C . The question is whether we ca... Read More about Editing to a Planar Graph of Given Degrees.

Bounding clique-width via perfect graphs (2016)
Journal Article
Dabrowski, K., Huang, S., & Paulusma, D. (2019). Bounding clique-width via perfect graphs. Journal of Computer and System Sciences, 104, 202-215. https://doi.org/10.1016/j.jcss.2016.06.007

We continue the study into the clique-width of graph classes defined by two forbidden induced graphs. We present three new classes of bounded clique-width and one of unbounded clique-width. The four new graph classes have in common that one of their... Read More about Bounding clique-width via perfect graphs.