Planar graph

Known as: Pontryagin-Kuratowski theorem, Planer graph, Planar embedding of the graph 
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges… (More)
Wikipedia

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2007
Highly Cited
2007
As has become standard, the four color map problem will be considered in the dual sense as the problem of whether the vertices of… (More)
Is this relevant?
Highly Cited
2005
Highly Cited
2005
We study various properties of the random planar graph Rn, drawn uniformly at random from the classPn of all simple planar graphs… (More)
  • figure 1
Is this relevant?
Highly Cited
2001
Highly Cited
2001
The vertices of any n-vertex planar graph can be partitioned into three sets A, B, C such that no edge joins a vertex in A with a… (More)
Is this relevant?
Highly Cited
1996
Highly Cited
1996
Spectral partitioning methods use the Fiedler vector—the eigenvector of the second-smallest eigenvalue of the Laplacian matrix—to… (More)
  • figure 1
  • figure 2
  • figure 3
Is this relevant?
Highly Cited
1995
Highly Cited
1995
We consider the special case of the traveling salesman problem (TSP) in which the distance metric is the shortest-path metric of… (More)
  • figure 1
  • figure 2
  • figure 3
  • figure 4
Is this relevant?
Highly Cited
1991
Highly Cited
1991
We show that the game chromatic number of a planar graph is at most 33. More generally, there exists a function f: f\l --+ f\l so… (More)
  • figure 1
  • figure 2
  • figure 3
  • figure 4
  • figure 5
Is this relevant?
Highly Cited
1990
Highly Cited
1990
We show that each plane graph of order n 2 3 has a straight line embedding on the n-2 by n-2 grid. This embedding is computable… (More)
  • figure 1
  • figure 2
  • figure 4
  • figure 5
  • figure 6
Is this relevant?
Highly Cited
1986
Highly Cited
1986
We prove that for every planar graph H there is a number w such that every graph with no minor isomorphic to H can be constructed… (More)
Is this relevant?
Highly Cited
1977
Highly Cited
1977
Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(√n… (More)
  • figure 1
  • figure 2
Is this relevant?
Highly Cited
1976
Highly Cited
1976
A data structure called a PQ-tree is introduced. PQ-trees can be used to represent the permutations of a set U in which various… (More)
  • figure 1
  • figure 2
  • figure 3
  • figure 4
  • figure 7
Is this relevant?