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...

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...

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...

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...

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...

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...

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...

trivalent graphs. A bicubic graph is a cubic bipartite graph. In 1932, Ronald M. Foster began collecting examples of cubic symmetric graphs, forming the...

direction. Line graphs are claw-free, and the line graphs of bipartite graphs are perfect. Line graphs are characterized by nine forbidden subgraphs and...

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...

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...

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...

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...

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...

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...

particular, there is a bipartite "incidence graph" or "Levi graph" corresponding to every hypergraph, and conversely, every bipartite graph can be regarded as...

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...

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...

computer networking Complete bipartite graph (or biclique), a special bipartite graph where every vertex on one side of the bipartition is connected to every...

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...

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...

complete bipartite graphs remains unproven, as does an analogous formula for the complete graphs. The crossing number inequality states that, for graphs where...

In combinatorial mathematics, a Levi graph or incidence graph is a bipartite graph associated with an incidence structure. From a collection of points...

largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgraphs of a given size. It belongs...

Perfect graphs include many important graphs classes including bipartite graphs, chordal graphs, and comparability graphs. The complement of a graph has an...

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...

construction of the chromatic polynomial of a graph. The number of perfect matchings of a bipartite graph can be calculated using the principle. Given...

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...

mathematical field of graph theory, a convex bipartite graph is a bipartite graph with specific properties. A bipartite graph, (U ∪ V, E), is said to...

complete bipartite graph K3,3. The Robertson–Seymour theorem implies that an analogous forbidden minor characterization exists for every property of graphs that...