Let D be an edge-coloured digraph, V (D) will denote the set of vertices of D; a set N ⊆ V (D) is said to be a kernel by monochromatic paths of D if it satisfies the following two conditions: For every pair of different vertices u, v ∈ N there is no monochromatic directed path between them and; for every vertex x ∈ V (D) − N there is a vertex y ∈ N such that there is an xy -monochromatic direct...

Coloured Petri nets are imperative for studying bigger biological models, particularly, those which expose repetition of components. Such models can be easily scaled by minor changes of a few parameters. Similarly, studying certain biological phenomena necessitates the existence of discrete and continuous variables as well as continuous and stochastic processes in one and the same model. Thus, ...

We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices of N there is no monochromatic path between them and for every vertex v / ∈ N there is a monochromatic path from v to N . We denote...

A subgraph of an edge-coloured complete graph is called rainbow if all its edges have different colours. In 1980 Hahn conjectured that every properly edge-coloured complete graph Kn has a rainbow Hamiltonian path. Although this conjecture turned out to be false, it was widely believed that such a colouring always contains a rainbow cycle of length almost n. In this paper, improving on several e...

Coloured Petri nets are Petri nets in which attributes are associated with individual tokens. These attributes are called “colours”. The set of colours is finite. Colors can be modified during transition firings, and the same transition can perform diffcrcn t transformations for tokens of different colours. Colours can thus distinguish tokens, and this allows to “fold” similar subnets of a net ...

This paper attempts to create coloured semi-transparent shadow images that can be projected onto multiple screens simultaneously from different viewpoints. The inputs to this approach are a set of coloured shadow images and view angles, projection information and light configurations for the final projections. We propose a method to convert coloured semi-transparent shadow images to a 3D visual...