Outputs (71)

The price of connectivity for cycle transversals (2016)
Journal Article
Hartinger, T., Johnson, M., Milanič, M., & Paulusma, D. (2016). The price of connectivity for cycle transversals. European Journal of Combinatorics, 58, 203-224. https://doi.org/10.1016/j.ejc.2016.06.003

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 View the MathML source be... Read More about The price of connectivity for cycle transversals.

Smart grid-aware scheduling in data centres (2016)
Journal Article
Mäsker, M., Nagel, L., Brinkmann, A., Lotfifar, F., & Johnson, M. (2016). Smart grid-aware scheduling in data centres. Computer Communications, 96, 73-85. https://doi.org/10.1016/j.comcom.2016.04.021

In several countries the expansion and establishment of renewable energies result in widely scattered and often weather-dependent energy production, decoupled from energy demand. Large, fossil-fuelled power plants are gradually replaced by many small... Read More about Smart grid-aware scheduling in data centres.

A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs (2016)
Journal Article
Golovach, P., Johnson, M., Paulusma, D., & Song., J. (2017). A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs. Journal of Graph Theory, 84(4), 331-363. https://doi.org/10.1002/jgt.22028

For a positive integer k, a k-coloring of a graph inline image is a mapping inline image such that inline image whenever inline image. The COLORING problem is to decide, for a given G and k, whether a k-coloring of G exists. If k is fixed (i.e., it i... Read More about A Survey on the Computational Complexity of Coloring Graphs with Forbidden Subgraphs.

Filling the complexity gaps for colouring planar and bounded degree graphs (2016)
Presentation / Conference Contribution
Dabrowski, K. K., Dross, F., Johnson, M., & Paulusma, D. (2015, October). Filling the complexity gaps for colouring planar and bounded degree graphs. Presented at 26th International Workshop on Combinatorial Algorithms (IWOCA 2015), Verona, Italy

We consider a natural restriction of the List Colouring problem, k-Regular List Colouring, which corresponds to the List Colouring problem where every list has size exactly k. We give a complete classification of the complexity of k-Regular List Colo... Read More about Filling the complexity gaps for colouring planar and bounded degree 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.

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?.

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.

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.