Objective
Colourings in broad sense are decompositions of discrete objects into simpler subobjects. Due to its generality, graph colouring theory has a central position in discrete mathematics and numerous applications, especially in computer science (memory allocation, fault diagnosis) and scheduling theory. In their recent book "Graph Colouring Problems", Jensen and Toft, both from Odense, describe the state of the art of graph colouring theory and propose more than 200 unsolved colouring problems.
Participants in this proposal are graph theorists from Denmark (B. Toft, Odense), Germany (Walther, Stiebitz, et al., Ilmenau), Russia (Borodin, Kostochka, et al., Novosibirsk), the United Kingdom (Woodall, Nottingham) and from Ukraine (Vizing, Odessa). The contacts of these mathematicians have existed for thirty years. In the last five years the contacts became much more intensive and have led to about 15 joint publications and a number of outstanding advances; in particular, several research problems have been solved by the participants of the proposed project.
After his classic results in 1960-70th, Vizing had not worked on colourings until recently, when he came up with the distributive colouring and the colouring of mixed graphs.
A 3-year research programme is proposed to INTAS with emphasis on the following special fields of graph theory:
- Colouring problems for planar graphs and graphs on higher surfaces;
- Critical graphs and hypergraphs;
- List colouring and total colouring;
- Variable degeneracy extensions of list colouring results;
- Hadwiger and Hajos number;
- Applications of graph theory in scheduling.
It is the plan to identify interesting problems within this area and work on their solutions. Several participants in this proposal are world experts in the mathematics needed to create progress within graph colouring theory.
The objective of the project is to promote further productive joint research in the area of graph colourings of the teams from Germany (Walther, Stiebitz et al.), Russia (Borodin, Kostochka et al.), Denmark (Toft), England (Woodall) and Ukraine (Vizing) by means of correspondence on the Internet on a regular basis and periodical face-to-face meetings. Given present circumstances in the FSU, it is important to provide the FSU participants with individual support and computer equipment.
Administrative and managerial tasks will be carried out from the Technical University in Ilmenau.
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Coordinator
98684 Ilmenau
Germany
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