Mathematical Sciences: Structural Graph Theory

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Thomas 9623031 Thomas will carry out and supervise research in graph theory with emphasis on structural characterizations of various properties of graphs. Thomas will also develop efficient practical algorithms based on this research. The areas of interest are Hadwiger's conjecture, spatial embeddings of graphs, applications of graph theory to low-dimensional topology, generalizations of the four-color theorem, graphs on surfaces with particular emphasis on coloring and hamiltonicity, linkage and subdivision problems, and infinite graphs. Graph theory is a subdiscipline of combinatorics. Combinatorics attempts to find efficient methods to study how discrete collections of objects can be arranged. The behavior of discrete systems is extremely important to modern communications. For example, the design of large networks, such as those occurring in telephone systems, and the design of algorithms in computer science deal with discrete sets of objects, and this makes use of combinatorial research. In addition, enumerative information from combinatorics research has been of use in the design of geometric algorithms for problems in robotics and motion planning.