Improved bounds on the size of separators of toroidal graphs
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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