Connector colouring provided an intuitive semantics of Reo connectors which lead to effective implementation techniques, first based on computing colouring tables directly, and later on encodings of colouring into constraints. One weakness of the framework is that it operates globally, giving a colouring to all primitives of the connector in lock-step, including those not involved in the intera...

A tropical graph (H, c) consists of a graph H and a (not necessarily proper) vertex-colouring c of H. For a fixed tropical graph (H, c), the decision problem (H, c)-Colouring asks whether a given input tropical graph (G, c1) admits a homomorphism to (H, c), that is, a standard graph homomorphism of G to H that also preserves vertex-colours. We initiate the study of the computational complexity ...

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties edge-coloured graphs. A homomorphism from $G$ $H$ is a vertex-mapping that preserves adjacencies and edge-colours. consider property having fixed $H$. The question we are interested in is: given an $G$, can perform $k$ operations so resulting admits $H$? vertex-deletion, edge-deletion ...

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 Colouring restricted to planar graphs, planar bipartite graphs, planar triangle-free graphs and to planar graphs with no 4-cycles and no 5-cycles. We a...

A k-frugal colouring of a graph G is a proper colouring of the vertices of G such that no colour appears more than k times in the neighbourhood of a vertex. This type of colouring was introduced by Hind, Molloy and Reed in 1997. In this paper, we study the frugal chromatic number of planar graphs, planar graphs with large girth, and outerplanar graphs, and relate this parameter with several wel...

Many complex timetabling problems, such as university course timetabling [1, 2] and employee rostering [3], have an underpinning bounded graph colouring component, a pattern penalisation component and a number of side constraints. The bounded graph colouring component corresponds to hard constraints such as “each student attends all events of courses of his choice, no student can be in two room...

A vertex colouring of a graph is nonrepetitive on paths if there is no path v1, v2, . . . , v2t such that vi and vt+i receive the same colour for all i = 1, 2, . . . , t. We determine the maximum density of a graph that admits a k-colouring that is nonrepetitive on paths. We prove that every graph has a subdivision that admits a 4-colouring that is nonrepetitive on paths. The best previous boun...