dom’ reached anthesis most rapidly, while plants of ‘Mathilde Gütges’ and ‘Merritt’s Supreme’ were the slowest to f-lower. Table 2 represents days to anthesis and not days to salable color. In general, plants were salable, based on sepal color, ≈10 days before anthesis, so subtracting 10 days from data in Table 2 gives forcing times (from start to sale) for these cultivars when a 62F (17C) mini...

3-list colouring is an NP-complete decision problem. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving 3-list colouring on permutation graphs.

In this paper we propose a self-organizing method for the graph colouring problem. The proposed self-organizing method for the graph colouring extends the chemical casting model and makes it possible to find the number of colours needed to colour the graph. The self-organizing approach is needed to solve scheduling tasks in the applications of ad hoc networks. Nodes in ad hoc networks are usual...

We consider n-dimensional Euclidean lattice networks with nearest neighbour coupling architecture. The associated lattice dynamical systems are infinite systems of ordinary differential equations, the cells, indexed by the points in the lattice. A pattern of synchrony is a finite-dimensional flow-invariant subspace for all lattice dynamical systems with the given network architecture. These sub...

For many problems in Scheduling and Timetabling the choice of a mathematical programming formulation is determined by the formulation of the graph colouring component. This paper briefly surveys seven known integer programming formulations of vertex colouring and introduces a new formulation using “supernodes”. In the definition of George and McIntyre [SIAM J. Numer. Anal. 15 (1978), no. 1, 90–...

Software watermarking involves embedding a unique identifier within a piece of software, to discourage software theft. The global revenue loss due to software piracy was estimated to be more than $50 billion in 2008. We survey the proposed register allocation based algorithms for software watermarking. This family of static watermarks are constraint-based and embed the watermark in a solution t...

Given graphs F and G and a nonnegative integer k, a function n : V(F) ~ {1 . . . . . k} is a G k-colouring of F if no induced copy of G is monochromatic; F is G k-chromatic if F has a G k-colouring but no G (k 1)-colouring. Further, we say F is uniquely G k-colourable if F is G k-chromatic and, up to a permutation of colours, it has only one G k-colouring. Such notions are extensions of the wel...

In this paper two best known at the moment algorithms for finding the maximum clique is compared. A key technique that both algorithms rely on is using a heuristic vertex colouring. The only difference between those algorithms is a way of using vertex-colouring and this difference in the very important. The algorithms’ approaches are divided in this paper into two classes: reapplying vertex col...

The generalized graph colouring problem (GCOL) for a fixed integer k, and fixed classes of graphs P1, . . . ,Pk (usually describing some common graph properties), is to decide, for a given graph G, whether the vertex set of G can be partitioned into sets V1, . . . , Vk such that, for each i, the induced subgraph of G on Vi belongs to Pi. It can be seen that GCOL generalizes many natural colouri...

This paper considers the problem of online graph colouring. An algorithm for vertex-colouring graphs is said to be online if each vertex is irrevocably assigned a colour before later vertices are considered. We first introduce the problem formally and define a perfomance metric to evaluate the success of an online colouring algorithm. Then, several upper and lower bounds are presented on the pe...