Abstract
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 [2]. 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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References
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© 1989 Springer-Verlag Berlin Heidelberg
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Aleksandrov, L.G., Djidjev, H.N. (1989). Improved bounds on the size of separators of toroidal graphs. In: Djidjev, H. (eds) Optimal Algorithms. OA 1989. Lecture Notes in Computer Science, vol 401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51859-2_12
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DOI: https://doi.org/10.1007/3-540-51859-2_12
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Print ISBN: 978-3-540-51859-4
Online ISBN: 978-3-540-46831-8
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