# Planar graph

Known as: Pontryagin-Kuratowski theorem, Planer graph, Planar embedding of the graphÂ
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 edgesâ€¦Â (More)
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## Papers overview

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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 ofâ€¦Â (More)
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Highly Cited
2005
Highly Cited
2005
• J. Comb. Theory, Ser. B
• 2005
We study various properties of the random planar graph Rn, drawn uniformly at random from the classPn of all simple planar graphsâ€¦Â (More)
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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 aâ€¦Â (More)
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Highly Cited
1996
Highly Cited
1996
• FOCS
• 1996
Spectral partitioning methods use the Fiedler vectorâ€”the eigenvector of the second-smallest eigenvalue of the Laplacian matrixâ€”toâ€¦Â (More)
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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 ofâ€¦Â (More)
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Highly Cited
1991
Highly Cited
1991
• Planar Graphs
• 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 soâ€¦Â (More)
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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 computableâ€¦Â (More)
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Highly Cited
1986
Highly Cited
1986
• J. Comb. Theory, Ser. B
• 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 constructedâ€¦Â (More)
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Highly Cited
1977
Highly Cited
1977
• 18th Annual Symposium on Foundations of Computerâ€¦
• 1977
Any n-vertex planar graph has the property that it can be divided into components of roughly equal size by removing only O(âˆšnâ€¦Â (More)
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Highly Cited
1976
Highly Cited
1976
• J. Comput. Syst. Sci.
• 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 variousâ€¦Â (More)
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