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...
33 KB (4,087 words) - 12:39, 16 July 2024
In the mathematical field of graph theory, a complete bipartite graph or biclique is a special kind of bipartite graph where every vertex of the first...
12 KB (959 words) - 07:51, 18 July 2024
that matching. Finding a matching in a bipartite graph can be treated as a network flow problem. Given a graph G = (V, E), a matching M in G is a set...
23 KB (2,938 words) - 07:47, 18 July 2024
a proper subset of vertices to the size of the subset. bipartite A bipartite graph is a graph whose vertices can be divided into two disjoint sets such...
106 KB (15,667 words) - 12:01, 16 May 2024
problem in bipartite graphs. It was discovered independently, also in 1931, by Jenő Egerváry in the more general case of weighted graphs. A vertex cover...
24 KB (3,433 words) - 00:05, 30 April 2024
bipartite graphs. Every line graph of a bipartite graph is an induced subgraph of a rook's graph. Because line graphs of bipartite graphs are perfect...
59 KB (7,042 words) - 19:21, 6 May 2024
k-vertex-connected graph is often called simply a k-connected graph. A bipartite graph is a simple graph in which the vertex set can be partitioned into two sets...
28 KB (3,689 words) - 23:54, 26 July 2024
In the mathematical area of graph theory, a chordal bipartite graph is a bipartite graph B = (X,Y,E) in which every cycle of length at least 6 in B has...
8 KB (884 words) - 09:54, 18 August 2023
trivalent graphs. A bicubic graph is a cubic bipartite graph. In 1932, Ronald M. Foster began collecting examples of cubic symmetric graphs, forming the...
15 KB (1,777 words) - 20:46, 11 March 2024
Adjacency matrix (redirect from Adjacency matrix of a bipartite graph)
graphs typically use the former convention. The adjacency matrix A of a bipartite graph whose two parts have r and s vertices can be written in the form A...
20 KB (2,461 words) - 21:32, 22 July 2024
direction. Line graphs are claw-free, and the line graphs of bipartite graphs are perfect. Line graphs are characterized by nine forbidden subgraphs and...
43 KB (5,299 words) - 10:28, 5 July 2024
a bipartite graph. A graph is bipartite if and only if it contains no cycles of odd length. Since a tree contains no cycles at all, it is bipartite. Every...
26 KB (3,380 words) - 14:08, 24 July 2024
Edge coloring (category Graph coloring)
either its maximum degree Δ or Δ+1. For some graphs, such as bipartite graphs and high-degree planar graphs, the number of colors is always Δ, and for multigraphs...
65 KB (8,472 words) - 07:37, 16 July 2024
triangle-free graph with the maximum number of edges is a complete bipartite graph in which the numbers of vertices on each side of the bipartition are as equal...
21 KB (2,524 words) - 00:41, 1 August 2024
Hypergraph (redirect from Host graph)
particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, every bipartite graph can be regarded as...
47 KB (6,289 words) - 21:53, 8 March 2024
and the independent number α ( G ) {\displaystyle \alpha (G)} . In a bipartite graph with no isolated vertices, the number of vertices in a maximum independent...
29 KB (3,553 words) - 00:07, 29 May 2024
Hall's marriage theorem (category Matching (graph theory))
as the number of sets in the group. The graph theoretic formulation answers whether a finite bipartite graph has a perfect matching—that is, a way to...
21 KB (3,208 words) - 06:26, 15 June 2024
computer networking Complete bipartite graph (or biclique), a special bipartite graph where every vertex on one side of the bipartition is connected to every...
14 KB (1,244 words) - 14:52, 27 April 2024
In graph theory, a branch of mathematics, the Herschel graph is a bipartite undirected graph with 11 vertices and 18 edges. It is a polyhedral graph (the...
14 KB (1,617 words) - 07:10, 6 December 2023
generalizes the concept of a bipartite graph: if G is bipartite, and R is the set of vertices on one side of the bipartition, the set R is automatically...
4 KB (523 words) - 21:47, 25 August 2023
Perfect graphs include many important graphs classes including bipartite graphs, chordal graphs, and comparability graphs. The complement of a graph has an...
13 KB (1,512 words) - 23:08, 18 August 2023
K_{r})} and characterizes all graphs attaining this maximum; such graphs are known as Turán graphs. For non-bipartite graphs G {\displaystyle G} , the Erdős–Stone...
10 KB (1,360 words) - 09:43, 1 August 2022
complete bipartite graphs remains unproven, as does an analogous formula for the complete graphs. The crossing number inequality states that, for graphs where...
26 KB (3,149 words) - 07:32, 16 July 2024
In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points...
6 KB (600 words) - 05:49, 27 August 2022
Maximum cardinality matching (category Matching (graph theory))
special case of the maximum cardinality matching problem is when G is a bipartite graph, whose vertices V are partitioned between left vertices in X and right...
10 KB (1,317 words) - 19:11, 16 July 2024
vertex transitive graphs include the complete bipartite graphs K m , n {\displaystyle K_{m,n}} where m ≠ n, which includes the star graphs K 1 , n {\displaystyle...
5 KB (515 words) - 08:29, 18 August 2023
and the graph itself is said to have degree k. Similarly, a bipartite graph in which every two vertices on the same side of the bipartition as each other...
10 KB (1,274 words) - 05:10, 29 February 2024
construction of the chromatic polynomial of a graph. The number of perfect matchings of a bipartite graph can be calculated using the principle. Given...
39 KB (6,679 words) - 21:37, 12 July 2024
Exact cover (section Bipartite graph)
equivalent to an exact hitting set problem, an incidence matrix, or a bipartite graph. In computer science, the exact cover problem is a decision problem...
36 KB (4,325 words) - 22:08, 20 July 2024
soul Bipartite graph, in mathematics, a graph in which the vertices are partitioned into two sets and every edge has an endpoint in each set Bipartite uterus...
482 bytes (102 words) - 15:09, 1 June 2016