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» Pointed Drawings of Planar Graphs
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GD
2006
Springer
13 years 11 months ago
Partitions of Graphs into Trees
In this paper, we study the k-tree partition problem which is a partition of the set of edges of a graph into k edge-disjoint trees. This problem occurs at several places with appl...
Therese C. Biedl, Franz-Josef Brandenburg
COMGEO
2007
ACM
13 years 7 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-reg...
Vida Dujmovic, Matthew Suderman, David R. Wood
COMPGEOM
2010
ACM
14 years 13 days ago
Adding one edge to planar graphs makes crossing number hard
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
Sergio Cabello, Bojan Mohar
DAM
2006
124views more  DAM 2006»
13 years 7 months ago
Coloring copoints of a planar point set
To a set of n points in the plane, one can associate a graph that has less than n2 vertices and has the property that k-cliques in the graph correspond vertex sets of convex k-gon...
Walter Morris
ESA
2008
Springer
130views Algorithms» more  ESA 2008»
13 years 9 months ago
Linear Time Planarity Testing and Embedding of Strongly Connected Cyclic Level Graphs
Abstract. A level graph is a directed acyclic graph with a level assignment for each node. Such graphs play a prominent role in graph drawing. They express strict dependencies and ...
Christian Bachmaier, Wolfgang Brunner