We prove that every n-vertex graph of genus g and maximal degree k has an edge separator of size O(√gkn). The upper bound is best possible to within a constant factor. This extends known results on planar graphs and similar results about vertex separators. We apply the edge separator to the isoperimetric number problem, graph embeddings and lower bounds for crossing numbers.
CITATION STYLE
Sýkora, O., & Vrto, I. (1992). Edge separators for graphs of bounded genus with applications. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 570 LNCS, pp. 159–168). Springer Verlag. https://doi.org/10.1007/3-540-55121-2_15
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