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COMGEO
2007
ACM

Graph drawings with few slopes

9 years 11 months ago
Graph drawings with few slopes
The slope-number of a graph G is the minimum number of distinct edge slopes in a straight-line drawing of G in the plane. We prove that for Δ 5 and all large n, there is a Δ-regular n-vertex graph with slope-number at least n1− 8+ε Δ+4 . This is the best known lower bound on the slope-number of a graph with bounded degree. We prove upper and lower bounds on the slope-number of complete bipartite graphs. We prove a general upper bound on the slope-number of an arbitrary graph in terms of its bandwidth. It follows that the slope-number of interval graphs, cocomparability graphs, and AT-free graphs is at most a function of the maximum degree. We prove that graphs of bounded degree and bounded treewidth have slope-number at most O(logn). Finally we prove that every graph has a drawing with one bend per edge, in which the number of slopes is at most one more than the maximum degree. In a companion paper, planar drawings of graphs with few slopes are also considered. © 2006 Elsevier ...
Vida Dujmovic, Matthew Suderman, David R. Wood
Added 12 Dec 2010
Updated 12 Dec 2010
Type Journal
Year 2007
Where COMGEO
Authors Vida Dujmovic, Matthew Suderman, David R. Wood
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