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An example of a bipartite graph, with a maximum matching (blue) and minimum vertex cover (red) both of size six. 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.
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 graph of a convex polyhedron), and is the smallest polyhedral graph that does not have a Hamiltonian cycle, a cycle passing through all its vertices.
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]
As an example, in the 4-cycle (which is bipartite), the det A G = 1. In contrast, in the 3-cycle (which is not bipartite), det A G = 2. Each corner of FMP(G) satisfies a set of m linearly-independent inequalities with equality. Therefore, to calculate the corner coordinates we have to solve a system of equations defined by a square submatrix of ...
Many triangle-free graphs are not bipartite, for example any cycle graph C n for odd n > 3. By Turán's theorem, the n-vertex 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 as possible.
A former TD Bank employee based in Florida was arrested and charged with facilitating money laundering to Colombia, New Jersey's attorney general said on Wednesday, in the first such arrest since ...
It’s no wonder Jeff Bezos holds over $70 million in art — this alternative asset has outpaced the S&P 500 since 1995, delivering an average annual return of 11.4%. Here’s how everyday ...
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.