Distributed obstruction finding and fullerene research

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The equipment requested includes workstations for graduate and undergraduate students which will be publically available in our theory lab and some processors without monitors to enable extensive distributed computations for two research problems.One of the most famous theorem in graph theory is Kuratowski's theorem: if a graph cannot be drawn on a plane with no crossing lines then it must contain a subgraph homeomorphic to one of two graphs. One major ongoing goal of my research program is to find a similar theorem for a torus (a surface shaped like a doughnut). Extra computational resources would greatly facilitate searching for these and the ultimate goal of finding a computer-aided proof that the set of obstructions we have found is complete. Having a complete set of obstructions could be used to prove theorems about toroidal graphs and would give insight as to how to design simple, fast algorithms for drawing pictures of them.Fullerenes are all-carbon molecules whose structures are 3-regular planar graphs with face sizes five or six. We have developed a program, FuiGui to aid in the visualization of these molecules and their parameters. Our goal is to amass a large database of parameter information for all the small fullerenes in order to investigate correlations between these parameters and important chemical properties of fullerenes. Extra computational facilities are critical for collecting this data in a reasonable amount of time.