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.

On a conjecture of Mohar concerning Kempe equivalence of regular graphs (2018)
Journal Article
Bonamy, M., Bousquet, N., Feghali, C., & Johnson, M. (2019). On a conjecture of Mohar concerning Kempe equivalence of regular graphs. Journal of Combinatorial Theory, Series B, 135, 179-199. https://doi.org/10.1016/j.jctb.2018.08.002

Let G be a graph with a vertex colouring α. Let a and b be two colours. Then a connected component of the subgraph induced by those vertices coloured either a or b is known as a Kempe chain. A colouring of G obtained from α by swapping the colours on... Read More about On a conjecture of Mohar concerning Kempe equivalence of regular graphs.

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.

Erdős–Ko–Rado theorems for a family of trees (2018)
Journal Article
Feghali, C., Johnson, M., & Thomas, D. (2018). Erdős–Ko–Rado theorems for a family of trees. Discrete Applied Mathematics, 236, 464-471. https://doi.org/10.1016/j.dam.2017.10.009

A family of sets is intersecting if any two sets in the family intersect. Given a graph and an integer , let denote the family of independent sets of size of . For a vertex of , let denote the family of independent sets of size that contain . This fa... Read More about Erdős–Ko–Rado theorems for a family of trees.

Surjective H-colouring: New hardness results (2018)
Journal Article
Golovach, P., Johnson, M., Martin, B., Paulusma, D., & Stewart, A. (2019). Surjective H-colouring: New hardness results. Computability, 8(1), 27-42. https://doi.org/10.3233/com-180084

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.

Enclosings of decompositions of complete multigraphs in 2-factorizations (2018)
Journal Article
Feghali, C., & Johnson, M. (2018). Enclosings of decompositions of complete multigraphs in 2-factorizations. Journal of Combinatorial Designs, 26(5), 205-218. https://doi.org/10.1002/jcd.21601

Let k, m, n, λ, and μ be positive integers. A decomposition of math formula into edge-disjoint subgraphs math formula is said to be enclosed by a decomposition of math formula into edge-disjoint subgraphs math formula if math formula and, after a sui... Read More about Enclosings of decompositions of complete multigraphs in 2-factorizations.