Everything about Planar graph
Graph that can be embedded in the plane
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 intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph, or a planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Planar graphA 5-minute orientation
- Skim a recent paper: Generalized m-Polar Fuzzy Planar Graph and Its ApplicationInfluential work since 2022
- Pick up a classic book: Davenport-Zannier Polynomials and Dessins D'EnfantsThe most-reprinted book on the subject
- Read the landmark paper: Graph minors. V. Excluding a planar graphCited 529 times
- Go sideways: Outerplanar graphA closely related topic
- Go sideways: Fáry's theoremA closely related topic
📖 Definitions
Noun A graph which can be embedded in a plane in such a way that its edges only intersect at vertices, i.e., they do not cross each other.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Graph minors. V. Excluding a planar graph
Graph minors. III. Planar tree-width
Every Planar Graph Is 5-Choosable
Quickly Excluding a Planar Graph
Graph Minors. XVI. Excluding a non-planar graph
Planar graph coloring with an uncooperative partner
On simultaneous planar graph embeddings
Recurrence of planar graph limits
🆕 Influential since 2022
Generalized m-Polar Fuzzy Planar Graph and Its Application
Connectivity-aware Graph: A planar topology for 3D building surface reconstruction
An Improved Planar Graph Product Structure Theorem
Every planar graph with girth at least 5 is (1,9)-colorable
Edge metric dimension and mixed metric dimension of planar graph Qn
📚 Books worth reading
Davenport-Zannier Polynomials and Dessins D'EnfantsNikolai M. Adrianov, Fedor Pakovich · 2020- 📕Discrete geometry and algebraic combinatoricsAlexander Barg, O. R. Musin · 2014
- 📕Polytopes and Discrete GeometryGabriel Cunningham, Mark Mixer · 2021
- 📕Topology and Geometry of BiopolymersErica Flapan, Helen Wong · 2020
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Dual graph In the mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has…
- Steinitz's theorem In polyhedral combinatorics, a branch of mathematics, Steinitz's theorem is a characterization of the undirected graphs formed by the edges and vertices…
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