Improved bounds on the size of separators of toroidal graphs
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It is known that the set of vertices of any toroidal graph (graph of orientable genus 1) can be divided into two edge-disjoint sets of size no greater than 2/3 times the size of the original graph by deleting no more than √18 √n vertices . The paper improves the constant before √n in the above theorem to √12 by using the structure separation graph and gives a lower bound on the optimal constant that can replace √12.
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