1,721,185 research outputs found
Straight-line drawings of outerplanar graphs in O(dn log n) area
No full textAbstractWe show an algorithm for constructing O(dnlogn) area outerplanar straight-line drawings of n-vertex outerplanar graphs with degree d. Also, we settle in the negative a conjecture (Biedl, 2002 [1]) on the area requirements of outerplanar graphs by showing that snowflake graphs admit linear-area drawings
Every Collinear Set in a Planar Graph is Free
No full textWe show that if a planar graph G has a plane straight-line drawing in which a subset S
of its vertices are collinear, then for any set of points, X, in the plane with |X| = |S|,
there is a plane straight-line drawing of G in which the vertices in S are mapped
to the points in X. This solves an open problem posed by Ravsky and Verbitsky
(in: Proceedings of the 37th International Workshop on Graph-Theoretic Concepts
in Computer Science, arXiv:0806.0253). In their terminology, we show that every
collinear set is free.This result has applications in graph drawing, including untangling,
column planarity, universal point subsets, and partial simultaneous drawings
On Minimum Area Planar Upward Drawings of Directed Trees and Other Families of Directed Acyclic Graphs
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