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Transversals of subtree hypergraphs and the source location problem in digraphs (2008)
Journal Article
Heuvel van den, J., & Johnson, M. (2008). Transversals of subtree hypergraphs and the source location problem in digraphs. Networks, 51(2), 113-119. https://doi.org/10.1002/net.20206

A hypergraph H = (V,E) is a subtree hypergraph if there is a tree T on V such that each hyperedge of E induces a subtree of T. Since the number of edges of a subtree hypergraph can be exponential in n = |V|, one can not always expect to be able to fi... Read More about Transversals of subtree hypergraphs and the source location problem in digraphs.

Mixing 3-colourings in bipartite graphs (2007)
Presentation / Conference Contribution
Cereceda, L., van den Heuvel, J., & Johnson, M. (2007, June). Mixing 3-colourings in bipartite graphs. Presented at International Workshop on Graph-Theoretic Concepts in Computer Science, Dornburg, Germany

For a 3-colourable graph G, the 3-colour graph of G, denoted C3(G), is the graph with node set the proper vertex 3-colourings of G, and two nodes adjacent whenever the corresponding colourings differ on precisely one vertex of G. We consider the foll... Read More about Mixing 3-colourings in bipartite graphs.

Finding Paths between Graph Colourings: Computational Complexity and Possible Distances (2007)
Journal Article
Bonsma, P., Cereceda, L., van den Heuvel, J., & Johnson, M. (2007). Finding Paths between Graph Colourings: Computational Complexity and Possible Distances. Electronic Notes in Discrete Mathematics, 29, 463-469. https://doi.org/10.1016/j.endm.2007.07.073

Suppose we are given a graph G together with two proper vertex k-colourings of G, α and β. How easily can we decide whether it is possible to transform α into β by recolouring vertices of G one at a time, making sure we always have a proper k-colouri... Read More about Finding Paths between Graph Colourings: Computational Complexity and Possible Distances.

Amalgamations of factorizations of complete graphs (2007)
Journal Article
Johnson, M. (2007). Amalgamations of factorizations of complete graphs. Journal of Combinatorial Theory, Series B, 97(4), 597-611. https://doi.org/10.1016/j.jctb.2006.09.004

Let t be a positive integer, and let K=(k1,…,kt) and L=(l1,…,lt) be collections of nonnegative integers. A (t,K,L)-factorization of a graph is a decomposition of the graph into factors F1,…,Ft such that Fi is ki-regular and li-edge-connected. In this... Read More about Amalgamations of factorizations of complete graphs.

The computational complexity of the parallel knock-out problem (2006)
Presentation / Conference Contribution
Broersma, H., Johnson, M., Paulusma, D., & Stewart, I. (2006, March). The computational complexity of the parallel knock-out problem. Presented at 7th Latin American Theoretical Informatics Symposium (LATIN 2006), Valdivia, Chile

We consider computational complexity questions related to parallel knock-out schemes for graphs. In such schemes, in each round, each remaining vertex of a given graph eliminates exactly one of its neighbours. We show that the problem of whether, for... Read More about The computational complexity of the parallel knock-out problem.

The External Network Problem with edge- or arc-connectivity requirements (2005)
Presentation / Conference Contribution
van den Heuvel, J., & Johnson, M. (2004, August). The External Network Problem with edge- or arc-connectivity requirements. Presented at Combinatorial and Algorithmic Aspects of Networking (CAAN 2004), Banff, Alberta, Canada

The connectivity of a communications network can often be enhanced if the nodes are able, at some expense, to form links using an external network. In this paper, we consider the problem of how to obtain a prescribed level of connectivity with a mini... Read More about The External Network Problem with edge- or arc-connectivity requirements.

Amalgamations of factorizations of complete equipartite graphs, (2004)
Journal Article
Hilton, A., & Johnson, M. (2004). Amalgamations of factorizations of complete equipartite graphs,. Discrete Mathematics, 284(1-3), 157-175. https://doi.org/10.1016/j.disc.2003.11.030

Let t be a positive integer, and let L=(l1,…,lt) and K=(k1,…,kt) be collections of nonnegative integers. A graph has a (t,K,L) factorization if it can be represented as the edge-disjoint union of factors F1,…,Ft where, for 1it, Fi is ki-regular and a... Read More about Amalgamations of factorizations of complete equipartite graphs,.

Characterization of graphs with Hall number 2 (2004)
Journal Article
Eslachi, C., & Johnson, M. (2004). Characterization of graphs with Hall number 2. Journal of Graph Theory, 45(2), 81-100. https://doi.org/10.1002/jgt.10154

Hall's condition is a simple requirement that a graph G and list assignment L must satisfy if G is to have a proper L-colouring. The Hall number of G is the smallest integer m such that whenever the lists on the vertices each has size at least m and... Read More about Characterization of graphs with Hall number 2.