Genus, Treewidth, and Local Crossing NumberDujmović, Vida and Eppstein, David and Wood, David R. (2015) Genus, Treewidth, and Local Crossing Number. In: Graph Drawing and Network Visualization: 23rd International Symposium, GD 2015, September 2426, 2015 , pp. 8798(Official URL: http://dx.doi.org/10.1007/9783319272610_8). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319272610_8
AbstractWe consider relations between the size, treewidth, and local crossing number (maximum number of crossings per edge) of graphs embedded on topological surfaces. We show that an nvertex graph embedded on a surface of genus g with at most k crossings per edge has treewidth O(sqrt((g+1)(k+1)n)) and layered treewidth O((g+1)k), and that these bounds are tight up to a constant factor. As a special case, the kplanar graphs with n vertices have treewidth O(sqrt((k+1)n)) and layered treewidth O(k+1), which are tight bounds that improve a previously known O((k+1)^(3/4)n^(1/2)) treewidth bound. Additionally, we show that for g<m, every medge graph can be embedded on a surface of genus g with O((m/(g+1))log^(2)g) crossings per edge, which is tight to a polylogarithmic factor.
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