- #1
bogdan
- 188
- 0
What is the definition of a planar graph and which properties does it have ?
Planar Graphs: Definition & Properties
- Context: Undergrad
- Thread starter bogdan
- Start date
-
- Tags
- Definition Graphs Properties
Click For Summary
Discussion Overview
The discussion revolves around the definition and properties of planar graphs, exploring both intuitive and abstract definitions, as well as relevant theorems related to planarity. The scope includes theoretical aspects and references to literature on the topic.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant defines a planar graph as one that can be drawn in a plane without self-intersections, citing the inscribed pentagram as a simple nonplanar example.
- Another participant questions the possibility of defining a planar graph without referencing a plane, suggesting a focus on the relationships between graph components.
- Some participants mention the existence of theorems that determine the planarity of graphs, expressing interest in these theorems for further understanding.
- A participant references specific literature, including works by F. Harary and O. Ore, which discuss theorems related to graph planarity.
- Concerns are raised about the availability of the cited books, with one participant expressing difficulty in finding accessible resources online.
Areas of Agreement / Disagreement
Participants express varying views on the definition of planar graphs, with some focusing on intuitive definitions while others seek more abstract formulations. The discussion remains unresolved regarding the best approach to defining planarity without reference to a plane.
Contextual Notes
There are limitations regarding the availability of resources and the complexity of the information found online, which may hinder participants' understanding of planar graphs and their properties.
Who May Find This Useful
This discussion may be useful for students and researchers interested in graph theory, particularly those exploring the concepts of planarity and related theorems.
- #2
lethe
- 645
- 0
a planar graph is one which can be drawn in a plane with no self-intersections. i believe the simplest nonplanar graph is the inscribed pentagram.
- #3
bogdan
- 188
- 0
Well...I know that...
But isn't there an "abstract" definition which explains what a planar graph is without using the concept of "plan" ?
Only relations between the components of the graph...
But isn't there an "abstract" definition which explains what a planar graph is without using the concept of "plan" ?
Only relations between the components of the graph...
- #4
lethe
- 645
- 0
there are some theorems about when a graph is planar or not. but you want to do what now? define a planar graph without using a plane?
- #5
bogdan
- 188
- 0
Aaa...those theorems sound interesting...that's what I need...
Where can I find them ?
(I want to define a plane using a planar graph )
Where can I find them ?
(I want to define a plane using a planar graph )
- #6
rutwig
- 40
- 1
See the book of F. Harary. He gives a complete review starting from the famous theorem of Kuratowski. The booklet by O. Ore does also deal a bit with planarity of graphs.
- #7
bogdan
- 188
- 0
If only I could find those books...anyway...I fount something on the Internet...but it's so complicated...
- #8
rutwig
- 40
- 1
Originally posted by bogdan
If only I could find those books...anyway...I fount something on the Internet...but it's so complicated...
The books cited are not available on the net, since they were written in 1967 and 1968. However, have a look at
http://www.math.uni-hamburg.de/home/diestel/books/graph.theory/download.html
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