Graph Theory and New Tools for Computation
Graph theory has become one of the fundamental subjects in mathematics. This is mainly because of its wide applicability in other areas of science and the humanities, where graphs are used as mathematical models for various fundamental objects. The objects represented might be people (e.g., job scheduling), buses (e.g., traffic scheduling), computers (e.g., interconnection networks), warehouses (e.g., facility location), etc. One of the main driving forces for research in graph theory is theoretical computer science, and some of the problems that Canada Research Chair Dr. Bojan Mohar is tackling in his research program have been motivated by their possible use in computer science.
Dr. Mohar ranks among the leading discrete mathematicians in the world today, and his research at Simon Fraser University is providing world-class expertise to several groups and initiatives that use discrete mathematics as a research tool.
Dr. Mohar has made significant advances in topological and algebraic graph theory, graph minors, and colourings (which in graph theory involve the assignment of colours to certain objects (e.g., vertices, edges, faces) in a graph). His research in graph theory is aimed at developing a new geometric theory of graph embeddings that can generalize and unify several of his former results but on a higher level. Embeddings is mathematical jargon for knots, the theoretical knots of knot theory in topology, which is a branch of mathematics that focuses on the study of topological spaces, structures that permit us to formalize concepts such as connectedness and continuity.
Dr. Mohar is making a study of interconnections between graphs, topology and geometry, graph minors, colourings and nowhere-zero flows. In addition, he is working on developing algorithmic and computational tools in these areas. He hopes to find new links between a wide selection of results that he believes to be true but which have not yet been proved to be so. These mathematical statements, though diverse, still have much in common and may lead to solutions of other problems.