In graph theory, an undirected graph is an outerplanar graph if it can be drawn in the plane without crossings in such a way that all of the vertices belong to the unbounded face of the drawing. That is, no vertex is totally surrounded by edges. Alternatively, a graph G is outerplanar if the graph formed from G by adding a new vertex, with edges connecting it to all the other vertices, is a planar graph.
A maximal outerplanar graph is an outerplanar graph that cannot have any additional edges added to it while preserving outerplanarity. Every maximal outerplanar graph with n vertices has exactly 2n−3 edges, and every bounded face of a maximal outerplanar graph is a triangle.
History
Outerplanar graphs were first studied and named by Chartrand & Harary (1967), in connection with the problem of determining the planarity of graphs formed by using a perfect matching to connect two copies of a base graph (for instance, many of the generalized Petersen graphs are formed in this way from two copies of a cycle graph). As they showed, when the base graph is biconnected, a graph constructed in this way is planar if and only if its base graph is outerplanar and the matching forms a dihedral permutation of its outer cycle.
Maximal Outer Planar Graphs And Minimally Non-Outer Planar Graphs
published: 28 Jun 2021
V6GTU2S23 Characterization of outerplanar graphs
published: 16 Jun 2021
Outer Planar Graphs
published: 27 Jun 2021
Outerplanar Graphs.
In this video, we cover the following topics:
1) Equivalent conditions for the dual graph to be Eulerian.
2) Outerplanar graphs
3) The boundary of the outer face of a 2-connected outerplanar graph is a spanning cycle.
4) K_4 and K_{2,3} are planar but not outerplaner.
5) Every simple outerplanar graph has a vertex of degree at most 2.
published: 09 Sep 2023
V6GTU2S19 Nonplanar graphs and outerplanar graphs
published: 16 Jun 2021
Outerplanar Graphs - 31
This video was made for educational purposes. It may be used as such after obtaining written permission from the author.
published: 17 May 2016
Graph Theory: 59. Maximal Planar Graphs
In this video we define a maximal planar graph and prove that if a maximal planar graph has n vertices and m edges then m = 3n-6. We use this to show that any planar graph with n vertices has at most 3n-6 edges.
-- Bits of Graph Theory by Dr. Sarada Herke.
Related videos:
GT57 Planar Graphs - https://youtu.be/wnYtITkWAYA
GT58 Euler's Formula for Plane Graphs - http://youtu.be/5ywif1Zpeo4
For quick videos about Math tips and useful facts, check out my other channel
"Spoonful of Maths" - http://youtube.com/spoonfulofmaths
Video Production by: Giuseppe Geracitano (goo.gl/O8TURb)
published: 14 Apr 2015
The Giant Component and 2-Core in Sparse Random Outerplanar Graphs (AofA2020)
Presentation of *The Giant Component and 2-Core in Sparse Random Outerplanar Graphs* at the online version of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms.
Authors: Mihyun Kang, Michael Missethan
https://www.math.aau.at/AofA2020/papers/18/
published: 10 Aug 2023
Excluded Minors for Outerplanar Graphs - 32
This video was made for educational purposes. It may be used as such after obtaining written permission from the author.
In this video, we cover the following topics:
1) Equivalent conditions for the dual graph to be Eulerian.
2) Outerplanar graphs
3) The boundary of the outer fa...
In this video, we cover the following topics:
1) Equivalent conditions for the dual graph to be Eulerian.
2) Outerplanar graphs
3) The boundary of the outer face of a 2-connected outerplanar graph is a spanning cycle.
4) K_4 and K_{2,3} are planar but not outerplaner.
5) Every simple outerplanar graph has a vertex of degree at most 2.
In this video, we cover the following topics:
1) Equivalent conditions for the dual graph to be Eulerian.
2) Outerplanar graphs
3) The boundary of the outer face of a 2-connected outerplanar graph is a spanning cycle.
4) K_4 and K_{2,3} are planar but not outerplaner.
5) Every simple outerplanar graph has a vertex of degree at most 2.
In this video we define a maximal planar graph and prove that if a maximal planar graph has n vertices and m edges then m = 3n-6. We use this to show that any ...
In this video we define a maximal planar graph and prove that if a maximal planar graph has n vertices and m edges then m = 3n-6. We use this to show that any planar graph with n vertices has at most 3n-6 edges.
-- Bits of Graph Theory by Dr. Sarada Herke.
Related videos:
GT57 Planar Graphs - https://youtu.be/wnYtITkWAYA
GT58 Euler's Formula for Plane Graphs - http://youtu.be/5ywif1Zpeo4
For quick videos about Math tips and useful facts, check out my other channel
"Spoonful of Maths" - http://youtube.com/spoonfulofmaths
Video Production by: Giuseppe Geracitano (goo.gl/O8TURb)
In this video we define a maximal planar graph and prove that if a maximal planar graph has n vertices and m edges then m = 3n-6. We use this to show that any planar graph with n vertices has at most 3n-6 edges.
-- Bits of Graph Theory by Dr. Sarada Herke.
Related videos:
GT57 Planar Graphs - https://youtu.be/wnYtITkWAYA
GT58 Euler's Formula for Plane Graphs - http://youtu.be/5ywif1Zpeo4
For quick videos about Math tips and useful facts, check out my other channel
"Spoonful of Maths" - http://youtube.com/spoonfulofmaths
Video Production by: Giuseppe Geracitano (goo.gl/O8TURb)
Presentation of *The Giant Component and 2-Core in Sparse Random Outerplanar Graphs* at the online version of the 31st International Conference on Probabilistic...
Presentation of *The Giant Component and 2-Core in Sparse Random Outerplanar Graphs* at the online version of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms.
Authors: Mihyun Kang, Michael Missethan
https://www.math.aau.at/AofA2020/papers/18/
Presentation of *The Giant Component and 2-Core in Sparse Random Outerplanar Graphs* at the online version of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms.
Authors: Mihyun Kang, Michael Missethan
https://www.math.aau.at/AofA2020/papers/18/
In this video, we cover the following topics:
1) Equivalent conditions for the dual graph to be Eulerian.
2) Outerplanar graphs
3) The boundary of the outer face of a 2-connected outerplanar graph is a spanning cycle.
4) K_4 and K_{2,3} are planar but not outerplaner.
5) Every simple outerplanar graph has a vertex of degree at most 2.
In this video we define a maximal planar graph and prove that if a maximal planar graph has n vertices and m edges then m = 3n-6. We use this to show that any planar graph with n vertices has at most 3n-6 edges.
-- Bits of Graph Theory by Dr. Sarada Herke.
Related videos:
GT57 Planar Graphs - https://youtu.be/wnYtITkWAYA
GT58 Euler's Formula for Plane Graphs - http://youtu.be/5ywif1Zpeo4
For quick videos about Math tips and useful facts, check out my other channel
"Spoonful of Maths" - http://youtube.com/spoonfulofmaths
Video Production by: Giuseppe Geracitano (goo.gl/O8TURb)
Presentation of *The Giant Component and 2-Core in Sparse Random Outerplanar Graphs* at the online version of the 31st International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms.
Authors: Mihyun Kang, Michael Missethan
https://www.math.aau.at/AofA2020/papers/18/
In graph theory, an undirected graph is an outerplanar graph if it can be drawn in the plane without crossings in such a way that all of the vertices belong to the unbounded face of the drawing. That is, no vertex is totally surrounded by edges. Alternatively, a graph G is outerplanar if the graph formed from G by adding a new vertex, with edges connecting it to all the other vertices, is a planar graph.
A maximal outerplanar graph is an outerplanar graph that cannot have any additional edges added to it while preserving outerplanarity. Every maximal outerplanar graph with n vertices has exactly 2n−3 edges, and every bounded face of a maximal outerplanar graph is a triangle.
History
Outerplanar graphs were first studied and named by Chartrand & Harary (1967), in connection with the problem of determining the planarity of graphs formed by using a perfect matching to connect two copies of a base graph (for instance, many of the generalized Petersen graphs are formed in this way from two copies of a cycle graph). As they showed, when the base graph is biconnected, a graph constructed in this way is planar if and only if its base graph is outerplanar and the matching forms a dihedral permutation of its outer cycle.