Finding torus obstructions/graph theory and algorithms for chemistry

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Project 1: Finding the Torus Obstructions- A torus is a surface shaped like a doughnut. A topological obstruction for the torus is a graph G with minimum degree three that is not embeddable on the torus but for all edges e, G-e embeds on the torus. A minor order obstruction has the additional property that for all edges e, G contract e embeds on the torus. To date, we have found 249,227 topological obstructions and 17,354 minor order obstructions. The aims of our future research are to check the previous results using independent computations, to develop better computational tools so that the search can be extended, to search for patterns in the known obstructions so that they can expressed more succinctly, to generate and prove conjectures regarding the complete set of obstructions, and to use the insights gained for developing practical algorithms for torus embedding.