Graph families | Planar graphs

Outerplanar graph

In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing. Outerplanar graphs may be characterized (analogously to Wagner's theorem for planar graphs) by the two forbidden minors K4 and K2,3, or by their Colin de Verdière graph invariants.They have Hamiltonian cycles if and only if they are biconnected, in which case the outer face forms the unique Hamiltonian cycle. Every outerplanar graph is 3-colorable, and has degeneracy and treewidth at most 2. The outerplanar graphs are a subset of the planar graphs, the subgraphs of series–parallel graphs, and the circle graphs. The maximal outerplanar graphs, those to which no more edges can be added while preserving outerplanarity, are also chordal graphs and visibility graphs. (Wikipedia).

Outerplanar graph
Video thumbnail

Find the feasible region by graphing 4 linear inequalities

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of Inequalities by Graphing

Video thumbnail

Graphing the system of two linear inequalities with two horizontal line

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of Inequalities by Graphing

Video thumbnail

How to determine the solution of a system of linear inequalities by graphing

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of inequalities by Graphing | Standard Form

Video thumbnail

Learn how to graph a system of two linear inequalities when the slope is 1

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of inequalities by Graphing | Standard Form

Video thumbnail

How to graph a system of linear inequalities in slope intercept form

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of Inequalities by Graphing

Video thumbnail

How to graph and shade a system of linear inequalities

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of Inequalities by Graphing

Video thumbnail

How to graph the system of linear inequalities of one horizontal and one vertical

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of Inequalities by Graphing

Video thumbnail

Learn how to graph a system of linear inequalities of two vertical boundary lines

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of Inequalities by Graphing

Video thumbnail

Graphing a system of two inequalities to determine the feasible region

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of Inequalities by Graphing

Video thumbnail

Irina Gelbukh 2023: The Reeb graph of a smooth function encodes the function class and manifold type

Title: How the Reeb graph of a smooth function encodes the class of the function and the type of the manifold Abstract: The Reeb graph of a function is a space obtained by contracting connected components of the function's level sets to points. Computer scientists mostly deal with Morse f

From playlist Vietoris-Rips Seminar

Video thumbnail

Graphs In Data Structures | Graph Representation In Data Structure | Data Structures | Simplilearn

This data structures tutorial is dedicated to helping beginners understand the graphs in data structures. In this tutorial, you will understand the fundamentals and terminologies of the graph data structure, their types and their representation using different methods. The graphs in this t

From playlist Data Structures & Algorithms [2022 Updated]

Video thumbnail

What are Planar Graphs? | Graph Theory

What are planar graphs? How can we draw them in the plane? In today's graph theory lesson we'll be defining planar graphs, plane graphs, regions of plane graphs, boundaries of regions of plane graphs, and introducing Euler's formula for connected plane graphs. A planar graph is a graph t

From playlist Graph Theory

Video thumbnail

Lecture 19 - Degree Sequences & Invariants

This is Lecture 19 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2019.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

Video thumbnail

Empty Graph, Trivial Graph, and the Null Graph | Graph Theory

Whenever we talk about something that is defined by sets, it is important to consider the empty set and how it fits into the definition. In graph theory, empty sets in the definition of a particular graph can bring on three types/categories of graphs. The empty graphs, the trivial graph, a

From playlist Graph Theory

Video thumbnail

What is the limit of a sequence of graphs?? | Benjamini-Schramm Convergence

This is an introduction to the mathematical concept of Benjamini-Schramm convergence, which is a type of graph limit theory which works well for sparse graphs. We hope that most of it is understandable by a wide audience with some mathematical background (including some prior exposure to g

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Vertex Cuts in Graphs (and a bit on Connectivity) | Graph Theory, Vertex-Connectivity

What is a vertex cut of a graph? And how can we use vertex cuts to describe how connected a graph is? We have discussed cut vertices and connected graphs before, but by tying them together in a way, we are able to characterize different levels of connectivity in graphs. The focus of this l

From playlist Graph Theory

Video thumbnail

Vertex Connectivity of a Graph | Connectivity, K-connected Graphs, Graph Theory

What is vertex connectivity in graph theory? We'll be going over the definition of connectivity and some examples and related concepts in today's video graph theory lesson! The vertex connectivity of a graph is the minimum number of vertices you can delete to disconnect the graph or make

From playlist Graph Theory

Video thumbnail

Lecture 10 - Data Structures for Graphs

This is Lecture 10 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 2007. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/2007/lecture10.pdf More informa

From playlist CSE373 - Analysis of Algorithms - 2007 SBU

Video thumbnail

Lecture 20 - Trees and Connectivity

This is Lecture 20 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2020.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

Video thumbnail

Graphing a linear system of linear inequalities

👉 Learn how to graph a system of inequalities. A system of inequalities is a set of inequalities which are collectively satisfied by a certain range of values for the variables. To graph a system of inequalities, each inequality making up the system is graphed individually with the side of

From playlist Solve a System of inequalities by Graphing | Standard Form

Related pages

Boxicity | Discrete Applied Mathematics | Intersection graph | Generalized Petersen graph | Perfect matching | Planar graph | Visibility graph | Vizing's theorem | Halin graph | Discrete Mathematics (journal) | Cactus graph | Linkless embedding | Greedy coloring | Colin de Verdière graph invariant | Dynamic programming | Chordal graph | Homeomorphism (graph theory) | Series–parallel graph | Degree (graph theory) | Triangle-free graph | Tree (graph theory) | Wagner's theorem | Symposium on Theoretical Aspects of Computer Science | Biconnected graph | Graph theory | International Journal of Computational Geometry and Applications | Complete bipartite graph | Simple polygon | Cycle graph | Dihedral group | Circle graph | Complete graph | Cycle (graph theory) | Euclidean plane | Kuratowski's theorem | Biconnected component | Forbidden graph characterization | Graph coloring | K-tree | Treewidth | Journal of Combinatorial Theory | Degeneracy (graph theory) | Ars Combinatoria (journal) | 1-planar graph | K-outerplanar graph | Graph embedding | Pancyclic graph | Crossing number (graph theory) | Polygon triangulation