Search results
Results from the WOW.Com Content Network
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.
Example 1 of Bipartite Graph. Let’s consider a simple example of a bipartite graph with 4 vertices, as shown in the following figure: In this graph, the vertices can be divided into two disjoint sets, {A, C} and {B, D}, such that every edge connects a vertex in one set to a vertex in the other set. Therefore, this graph is a bipartite graph.
Bipartite graphs are a special type of graph where the nodes can be divided into two distinct sets, with no edges connecting nodes within the same set. Every edge connects a node from the first set to a node in the second set.
A bipartite graph, also called a bigraph, is a set of graph vertices decomposed into two disjoint sets such that no two graph vertices within the same set are adjacent. A bipartite graph is a special case of a k-partite graph with k=2.
our discussion of graph coloring. Example 2. For m;n 2N, the graph G with V(G) = [m+ n] and E(G) = fij ji 2[m] and j 2[m+ n] n[m]g is clearly a bipartite graph on the (disjoint) parts [m] and [m+n]n[m]. This graph is called the complete bipartite graph on the parts [m] and [m+n]n[m], and it is denoted by K m;n. Example 3. Let C n by the cyclic ...
For example, what can we say about Hamilton cycles in simple bipartite graphs? Suppose the partition of the vertices of the bipartite graph is \(X\) and \(Y\). Because any cycle alternates between vertices of the two parts of the bipartite graph, if there is a Hamilton cycle then \(|X|=|Y|\ge2\).
A matching in a bipartite graph G = (X; ; Y ) is a subset M of , such that no two edges of M meet at a single vertex. Here are two matchings: f(x1; y1); (x3; y3)g and f(x1; y1); (x3; y2); (x4; y3)g. vertices which are not part of an edge in M are called free.
This paper will begin with a brief introduction to the theory of graphs and will focus primarily on the properties of bipartite graphs. The final section will demonstrate how to use bipartite graphs to solve problems.
Definition. A graph G is bipartite if it is the trivial graph or if its vertex set can be partitioned into two independent, non-empty sets A and B. We refer to { A, B } as a bipartiton of V(G). Note: Some people require a bipartite graph to be non-trivial. Examples include any even cycle, any tree, and the graph below.
Bipartite graphs are very useful objects to denote relations between two classes of objects: agents-items, jobs-machines, students-courses, etc. For example, suppose we have a set of students and a set of offered classes.