# Category: Bipartite graphs

Modular graph
In graph theory, a branch of mathematics, the modular graphs are undirected graphs in which every three vertices x, y, and z have at least one median vertex m(x, y, z) that belongs to shortest paths b
Bipartite double cover
In graph theory, the bipartite double cover of an undirected graph G is a bipartite, covering graph of G, with twice as many vertices as G. It can be constructed as the tensor product of graphs, G × K
Convex bipartite graph
In the 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 be convex over the vertex set U if U can be
Median graph
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest paths betwe
Bipartite half
In graph theory, the bipartite half or half-square of a bipartite graph G = (U,V,E) is a graph whose vertex set is one of the two sides of the bipartition (without loss of generality, U) and in which
Zarankiewicz problem
The Zarankiewicz problem, an unsolved problem in mathematics, asks for the largest possible number of edges in a bipartite graph that has a given number of vertices and has no complete bipartite subgr
Tree (graph theory)
In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. A forest is an undirected graph in whi
Walther graph
In the mathematical field of graph theory, the Walther graph, also called the Tutte fragment, is a planar bipartite graph with 25 vertices and 31 edges named after Hansjoachim Walther. It has chromati
Bipartite network projection
Bipartite network projection is an extensively used method for compressing information about bipartite networks. Since the one-mode projection is always less informative than the original bipartite gr
Chordal bipartite graph
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 a chord, i.e., an edge that connects two vertice
Simplex graph
In graph theory, a branch of mathematics, the simplex graph κ(G) of an undirected graph G is itself a graph, with one node for each clique (a set of mutually adjacent vertices) in G. Two nodes of κ(G)
Bipartite dimension
In the mathematical fields of graph theory and combinatorial optimization, the bipartite dimension or biclique cover number of a graph G = (V, E) is the minimum number of bicliques (that is complete b
Bipartite graph
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
Bipartite realization problem
The bipartite realization problem is a classical decision problem in graph theory, a branch of combinatorics. Given two finite sequences and of natural numbers, the problem asks whether there is label
Squaregraph
In graph theory, a branch of mathematics, a squaregraph is a type of undirected graph that can be drawn in the plane in such a way that every bounded face is a quadrilateral and every vertex with thre
Partial cube
In graph theory, a partial cube is a graph that is isometric to a subgraph of a hypercube. In other words, a partial cube can be identified with a subgraph of a hypercube in such a way that the distan
Kőnig's theorem (graph theory)
In the mathematical area of graph theory, Kőnig's theorem, proved by Dénes Kőnig, describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs
Biregular graph
In graph-theoretic mathematics, a biregular graph or semiregular bipartite graph is a bipartite graph for which every two vertices on the same side of the given bipartition have the same degree as eac
Quasi-bipartite graph
In the mathematical field of graph theory, an instance of the Steiner tree problem (consisting of an undirected graph G and a set R of terminal vertices that must be connected to each other) is said t