Abstract
A planarizing set of a graph is a set of edges or vertices whose removal leaves a planar graph. It is shown that, if G is an n-vertex graph of maximum degree d and orientable genus g, then there exists a planarizing set of O(√dgn) edges. This result is tight within a constant factor. Similar results are obtained for planarizing vertex sets and for graphs embedded on nonorientable surfaces. Planarizing edge and vertex sets can be found in O(n+g) time, if an embedding of G on a surface of genus g is given. We also construct an approximation algorithm that finds an O(√gn log g) planarizing vertex set of G in O(n log g) time if no genus-g embedding is given as an input.
This work is partially supported by National Scientific Foundation grant CCR-9409191.
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Djidjev, H.N., Venkatesan, S.M. (1995). Planarization of graphs embedded on surfaces. In: Nagl, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 1995. Lecture Notes in Computer Science, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60618-1_66
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DOI: https://doi.org/10.1007/3-540-60618-1_66
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