Outputs (10)

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.

A multi-level hypergraph partitioning algorithm using rough set clustering (2015)
Book Chapter
Lotfifar, F., & Johnson, M. (2015). A multi-level hypergraph partitioning algorithm using rough set clustering. In J. Träff, S. Hunold, & F. Versaci (Eds.), Euro-Par 2015 : parallel processing : 21st International Conference on Parallel and Distributed Computing, Vienna, Austria, August 24-28, 2015, Proceedings (159-170). Springer Verlag. https://doi.org/10.1007/978-3-662-48096-0_13

The hypergraph partitioning problem has many applications in scientific computing and provides a more accurate inter-processor communication model for distributed systems than the equivalent graph problem. In this paper, we propose a sequential multi... Read More about A multi-level hypergraph partitioning algorithm using rough set clustering.

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.

Smart grid-aware scheduling in data centres (2015)
Presentation / Conference Contribution
Mäsker, M., Nagel, L., Brinkmann, A., Lotfifar, F., & Johnson, M. (2015, December). Smart grid-aware scheduling in data centres. Presented at 2015 Sustainable Internet and ICT for Sustainability (SustainIT), Madrid, Spain

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.