Explore: Bipartite Graphs

graphs, and every median graph is a partial cube. Bipartite graphs may be characterized in several different ways: An undirected graph is bipartite if

k-partite graphs and graphs that avoid larger cliques as subgraphs in Turán's theorem, and these two complete bipartite graphs are examples of Turán graphs, the

for special classes of graphs such as bipartite planar graphs, as described in the main article. In a weighted bipartite graph, the optimization problem

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

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

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

necessarily bipartite) graphs. It runs in time O ( | V | 2 ⋅ | E | ) {\displaystyle O(|V|^{2}\cdot |E|)} . A better performance of O(√VE) for general graphs, matching

("The spectrum of a graph"), pp. 7–13. Brouwer, Andries E.; Haemers, Willem H. (2012), "1.3.6 Bipartite graphs", Spectra of Graphs, Universitext, New York:

graph; perfect graphs include many well-known graph classes including the bipartite graphs, chordal graphs, and comparability graphs. In his 1961 and

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