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2. Bipartite graph - Wikipedia

   en.wikipedia.org/wiki/Bipartite_graph

   The degree sequence of a bipartite graph is the pair of lists each containing the degrees of the two parts and . For example, the complete bipartite graph K 3,5 has degree sequence (,,), (,,,,). Isomorphic bipartite graphs have the same degree sequence. However, the degree sequence does not, in general, uniquely identify a bipartite graph; in ...

3. Complete bipartite graph - Wikipedia

   en.wikipedia.org/wiki/Complete_bipartite_graph

   A complete bipartite graph K m,n has a maximum matching of size min{m,n}. A complete bipartite graph K n,n has a proper n-edge-coloring corresponding to a Latin square. [14] Every complete bipartite graph is a modular graph: every triple of vertices has a median that belongs to shortest paths between each pair of vertices. [15]

4. List coloring - Wikipedia

   en.wikipedia.org/wiki/List_coloring

   For a graph G, let χ(G) denote the chromatic number and Δ(G) the maximum degree of G.The list coloring number ch(G) satisfies the following properties.. ch(G) ≥ χ(G).A k-list-colorable graph must in particular have a list coloring when every vertex is assigned the same list of k colors, which corresponds to a usual k-coloring.

5. Graph (discrete mathematics) - Wikipedia

   en.wikipedia.org/wiki/Graph_(discrete_mathematics)

   In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called vertices (also called nodes or points ) and each of the related pairs of vertices is called an edge (also called link or line ...

6. Turán's brick factory problem - Wikipedia

   en.wikipedia.org/wiki/Turán's_brick_factory_problem

   In the mathematics of graph drawing, Turán's brick factory problem asks for the minimum number of crossings in a drawing of a complete bipartite graph. The problem is named after Pál Turán, who formulated it while being forced to work in a brick factory during World War II. [1]

7. Biregular graph - Wikipedia

   en.wikipedia.org/wiki/Biregular_graph

   In graph-theoretic mathematics, a biregular graph [1] or semiregular bipartite graph [2] is a bipartite graph = (,,) for which every two vertices on the same side of the given bipartition have the same degree as each other.