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GD
1998
Springer
13 years 10 months ago
Geometric Thickness of Complete Graphs
We define the geometric thickness of a graph to be the smallest number of layers such that we can draw the graph in the plane with straightline edges and assign each edge to a lay...
Michael B. Dillencourt, David Eppstein, Daniel S. ...
GD
2007
Springer
14 years 3 days ago
A Bipartite Strengthening of the Crossing Lemma
Let G = (V, E) be a graph with n vertices and m ≥ 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Ω(m3 /n2 ) pairs of crossing edges; or ...
Jacob Fox, János Pach, Csaba D. Tóth
COMBINATORICA
2008
97views more  COMBINATORICA 2008»
13 years 6 months ago
Pfaffian labelings and signs of edge colorings
Abstract. We relate signs of edge-colorings (as in classical Penrose's result) with "Pfaffian labelings", a generalization of Pfaffian orientations, whereby edges ar...
Serguei Norine, Robin Thomas
GD
2006
Springer
13 years 9 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
CLA
2004
13 years 7 months ago
Planarity of Additively Drawn Concept Lattices
In Formal Concept Analysis, it is a very important but quite difficult task to draw line diagrams of concept lattices automatically. In particular, we want every planar lattice to ...
Christian Zschalig