Graph families | Parity (mathematics) | Bipartite graphs
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is every edge connects a vertex in to one in . Vertex sets and are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets and may be thought of as a coloring of the graph with two colors: if one colors all nodes in blue, and all nodes in red, each edge has endpoints of differing colors, as is required in the graph coloring problem. In contrast, such a coloring is impossible in the case of a non-bipartite graph, such as a triangle: after one node is colored blue and another red, the third vertex of the triangle is connected to vertices of both colors, preventing it from being assigned either color. One often writes to denote a bipartite graph whose partition has the parts and , with denoting the edges of the graph. If a bipartite graph is not connected, it may have more than one bipartition; in this case, the notation is helpful in specifying one particular bipartition that may be of importance in an application. If , that is, if the two subsets have equal cardinality, then is called a balanced bipartite graph. If all vertices on the same side of the bipartition have the same degree, then is called biregular. (Wikipedia).
What is a Bipartite Graph? | Graph Theory
What is a bipartite graph? We go over it in today’s lesson! I find all of these different types of graphs very interesting, so I hope you will enjoy this lesson. A bipartite graph is any graph whose vertex set can be partitioned into two disjoint sets (called partite sets), such that all e
From playlist Graph Theory
What are Complete Bipartite Graphs? | Graph Theory, Bipartite Graphs
What are complete bipartite graphs? We'll define complete bipartite graphs and show some examples and non-examples in today's video graph theory lesson! Remember a graph G = (V, E) is bipartite if the vertex set V can be partitioned into two sets V1 and V2 (called partite sets) such that
From playlist Graph Theory
Bipartite Graphs with Isolated Vertices | Graph Theory, Complete Bipartite Graphs
We know what a bipartite graph is, and we know about complete bipartite graphs. But how do these definitions work with isolated vertices that have no neighbors? We'll go over just that in today's graph theory lesson! Remember that a bipartite graph is a graph whose vertices that can be pa
From playlist Graph Theory
OCR MEI MwA D: Graph Theory: 07 Bipartite Graphs
https://www.buymeacoffee.com/TLMaths Navigate all of my videos at https://sites.google.com/site/tlmaths314/ Like my Facebook Page: https://www.facebook.com/TLMaths-1943955188961592/ to keep updated Follow me on Instagram here: https://www.instagram.com/tlmaths/ Many, MANY thanks to Dea
From playlist OCR MEI MwA D: Graph Theory
From playlist Graph Theory
Bipartite Graphs: Determine a Matching of A if Possible
This video explains how to determine a matching of A in a bipartite and how to use Hall's Marriage theorem to explain why there I not a matching of A in a graph. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Every Tree is a Bipartite Graph
This video explains how to show that a tree is a bipartite graph. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Introduction to Matching in Bipartite Graphs (Hall's Marriage Theorem)
This video introduces matching in bipartite graphs. mathispower4u.com
From playlist Graph Theory (Discrete Math)
Bipartite Graphs and Named Graphs
The lesson explains bipartite and complete bipartite graphs. Then common named graphs are defined. mathispower4u.com
From playlist Graph Theory (Discrete Math)
How to Tell if Graph is Bipartite (by hand) | Graph Theory
How can we tell if a graph is bipartite by hand? We'll discuss the easiest way to identify bipartite graphs in today's graph theory lesson. This method takes advantage of the fact that bipartite graphs are 2-colorable. This means their vertices can be colored using only two colors so adjac
From playlist Graph Theory
Proof: A Graph or its Complement is not Bipartite | Graph Theory, Bipartite Graphs
If G is a graph with at least 5 vertices, at most one of G or G complement is bipartite. We will prove this graph theory result directly using the well know bipartite graph theorem relating to odd cycles. The only way the statement is false is if there exists a graph G of order 5 or more
From playlist Graph Theory
Chromatic Number of Bipartite Graphs | Graph Theory
What is the chromatic number of bipartite graphs? If you remember the definition, you may immediately think the answer is 2! This is practically correct, though there is one other case we have to consider where the chromatic number is 1. We'll explain both possibilities in today's graph th
From playlist Graph Theory
Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o
From playlist CMU 21-228 Discrete Mathematics
Proof: If a Graph has no Odd Cycles then it is Bipartite | Graph Theory, Bipartite Theorem
A graph has no odd cycles if and only if it is bipartite. One direction, if a graph is bipartite then it has no odd cycles, is pretty easy to prove. The other direction, if a graph has no odd cycles then it is bipartite, is quite a bit harder to prove! In this video, we focus on the diffic
From playlist Graph Theory
Extremal theory of ordered graphs – Gábor Tardos – ICM2018
Combinatorics Invited Lecture 13.3 Extremal theory of ordered graphs Gábor Tardos Abstract: We call simple graphs with a linear order on the vertices ‘ordered graphs’. Turán-type extremal graph theory naturally extends to ordered graphs. This is a survey on the ongoing research in the ex
From playlist Combinatorics
Discrete Math II - 10.2.2 Special Graphs: Bipartite Graphs
This video is a deeper look at bipartite graphs. We look at both the definition of a bipartite graph and using graph coloring to determine if an existing graph can be redrawn as bipartite. In addition, we model real-life scenarios with bipartite graphs in an effort to create a complete mat
From playlist Discrete Math II/Combinatorics (entire course)
AQA Decision 1 6.01 Introducing Bipartite Graphs and Adjacency Matrices
I introduce the concept of bipartite graphs and how these can be represented using an adjacency matrix.
From playlist [OLD SPEC] TEACHING AQA DECISION 1 (D1)