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...

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...

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...

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

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...

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

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...

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

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...

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

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...

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...

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...

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

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...

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...

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...

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...

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...

of graph theory topics, by Wikipedia page. See glossary of graph theory for basic terminology Amalgamation Bipartite graph Complete bipartite graph Disperser...

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

can be formalized as a problem in topological graph theory by asking whether the complete bipartite graph K 3 , 3 {\displaystyle K_{3,3}} , with vertices...

In graph theory, a star Sk is the complete bipartite graph K1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when...

mathematical fields of graph theory and combinatorial optimization, the bipartite dimension or biclique cover number of a graph G = (V, E) is the minimum...