Title: Theory / Unimportant / CS / Fundamental / Graph / Bondy - Murty / 10 Planar
Tags: récupéré examplesSwitchExample1

Name: A planar graph
Page: 243
Chapter: 10
Section: 1
Name2: A graph embeddable in the plane
Intuition: A graph which can be dran in the plane so that its edges intersect only at their ends

Name: A planar embedding of \(G\)
Page: 243
Chapter: 10
Section: 1
Variables: \(G\) a graph
Example: for \(K_5\setminus e\):
Intuition: A planar copy of \(G\) on a plane
Denoted by: \(\tilde G\)

Name: A plane graph
Definition: A planar embedding of a planar graph
Page: 244
Chapter: 10
Section: 1

Name: The point \(v\)
Definition: the element of \(\tilde G\) representing \(v\)
Page: 244
Chapter: 10
Section: 1
Variables: \(G\) a planar graph
\(\tilde G\) a plane embedding
\(v\in V(G)\)
Context: Planar embedding

Name: The line \(e\)
Definition: the element of \(\tilde G\) representing \(e\)
Page: 244
Chapter: 10
Section: 1
Variables: \(G\) a planar graph
\(\tilde G\) a plane embedding
\(e\in E(G)\)

Name: A curve
Definition: A continuous image of \([0,1]\)
Page: 244
Chapter: 10
Section: 1
Intuition: Something drawn without removing the pen from the paper

Name: A closed curve
Definition: A continuous image of \([0,1]\) with the image of \(0\) and 1 equals
Page: 244
Chapter: 10
Section: 1

Name: A simple curve
Definition: A curve injective on \([0,1)\)
Page: 244
Chapter: 10
Section: 1
Intuition: A curve which does not intersect itself

Name: An arcwise connected subset of the plane
Definition: A subset of the plane such that there is a curve from any point to any other point
Page: 244
Chapter: 10
Section: 1

Question: \(C\) defines
Answer: a partition of the plane into interior and exterior
Page: 245, 26
Chapter: 10, 0 stillwell
Section: 1, 3.1
Variables: \(C\) a closed curve
Index: 1
Kind: Theo
Name: The Jordan Curve Theorem

Name: The interior of the plane defined by \(C\)
Page: 245
Chapter: 10
Section: 1
Variables: \(C\) a closed curve
Kind: Theo
Abbreviation: \(\mathrm{int}(C)\)
Assuming: \(C\) is simple

Definition: The closure of the interior of the plane defined by \(C\)
Page: 245
Chapter: 10
Section: 1
Variables: \(C\) a closed curve
Notation: \(\mathrm{Int}(C)\)
Kind: Theo
Assuming: \(C\) is simple

Definition: The closure of the exterior of the plane defined by \(C\)
Page: 245
Chapter: 10
Section: 1
Variables: \(C\) a closed curve
Notation: \(\mathrm{Ext}(C)\)
Kind: Theo
Assuming: \(C\) is simple

Definition: The exterior of the plane defined by \(C\)
Page: 245
Chapter: 10
Section: 1
Variables: \(C\) a closed curve
Context: Closed curve
Notation: \(\mathrm{ext}(C)\)
Kind: Theo
Example: \(K_{3,3}\)
Assuming: \(C\) is simple

Name: A nonplanar graph
Definition: A graph which is not planar
Page: 245
Chapter: 10
Section: 1
Index: 2
Kind: Theo
Example: \(K_5\)