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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
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
CORR
2008
Springer
131views Education» more  CORR 2008»
13 years 7 months ago
Deterministically Isolating a Perfect Matching in Bipartite Planar Graphs
We present a deterministic way of assigning small (log bit) weights to the edges of a bipartite planar graph so that the minimum weight perfect matching becomes unique. The isolati...
Samir Datta, Raghav Kulkarni, Sambuddha Roy
GD
2006
Springer
13 years 11 months ago
Planar Decompositions and the Crossing Number of Graphs with an Excluded Minor
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
David R. Wood, Jan Arne Telle