h-Quasi Planar Drawings of Bounded Treewidth Graphs in Linear Area
نویسندگان
چکیده
We study the problem of computing h-quasi planar drawings in linear area; in an h-quasi planar drawing the number of mutually crossing edges is bounded by a constant h. We prove that every n-vertex partial k-tree admits a straight-line h-quasi planar drawing in O(n) area, where h depends on k but not on n. For specific sub-families of partial k-trees, we present ad-hoc algorithms that compute h-quasi planar drawings in linear area, such that h is significantly reduced with respect to the general result.
منابع مشابه
Beyond Outerplanarity
We study straight-line drawings of graphs where the vertices are placed in convex position in the plane, i.e., convex drawings. We consider two families of graph classes with nice convex drawings: outer k-planar graphs, where each edge is crossed by at most k other edges; and, outer k-quasi-planar graphs where no k edges can mutually cross. We show that the outer k-planar graphs are (b √ 4k + 1...
متن کاملReally Straight Graph Drawings
We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with ...
متن کاملPlanar Graphs and Partial k-Trees
It is well-known that many NP-hard problems can be solved efficiently on graphs of bounded treewidth. We begin by showing that Knuth’s results on nested satisfiability are easily derived from this fact since nested satisfiability graphs have treewidth at most three. Noting that nested satisfiability graphs have a particular form of planar drawing, we define a more general form of graph drawing ...
متن کاملReally Straight Drawings II: Non-Planar Graphs
We study straight-line drawings of non-planar graphs with few slopes. Interval graphs, co-comparability graphs and AT-free graphs are shown to have have drawings in which the number of slopes is bounded by the maximum degree. We prove that graphs of bounded degree and bounded treewidth have drawings with O(log n) slopes. Finally we prove that every graph has a drawing with one bend per edge, in...
متن کاملar X iv : c s / 04 05 11 2 v 1 [ cs . D M ] 3 1 M ay 2 00 4 Really Straight Graph Drawings ∗
We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane drawing ...
متن کامل