Skip to search formSkip to main contentSkip to account menu
You are currently offline. Some features of the site may not work correctly.

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… 
Wikipedia

Papers overview

Semantic Scholar uses AI to extract papers important to this topic.
Highly Cited
2000
Highly Cited
2000
Suppose that $G_j$ is a sequence of finite connected planar graphs, and in each $G_j$ a special vertex, called the root, is… 
  • figure 2.1
  • figure 3.1
  • figure 3.2
Highly Cited
1995
Highly Cited
1995
We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are… 
  • figure 1
  • figure 2
  • figure 3
  • figure 4
  • figure 5
Highly Cited
1994
Highly Cited
1994
We prove the statement of the title, which was conjectured in 1975 by V. G. Vizing and, independently, in 1979 by P. Erdos, A. L… 
Highly Cited
1994
Highly Cited
1994
Abstract In an earlier paper, the first two authors proved that for any planar graph H , every graph with no minor isomorphic to… 
Highly Cited
1990
Highly Cited
1990
Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fáry embedding (i.e… 
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… 
  • figure 1
  • figure 2
  • figure 3
  • figure 4
  • figure 5
Highly Cited
1983
Highly Cited
1983
  • B. Baker
  • 24th Annual Symposium on Foundations of Computer…
  • 1983
  • Corpus ID: 9706753
This paper describes a general technique that can be used to obtain approximation algorithms for various NP-complete problems on… 
  • figure 1
  • figure 2
  • figure 3
  • figure 5
  • figure 6
Highly Cited
1979
Highly Cited
1979
Shimon Even's Graph Algorithms, published in 1979, was a seminal introductory book on algorithms read by everyone engaged in the… 
Highly Cited
1977
Highly Cited
1977
Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge… 
  • figure 1
  • figure 3
  • figure 5
  • figure 6
  • figure 7
Highly Cited
1977
Highly Cited
1977
When I first entered the world of Mathematics, I became aware of a strange and little-regarded sect of "Graph Theorists…