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2. Biclique-free graph - Wikipedia

   en.wikipedia.org/wiki/Biclique-free_graph

   A graph with degeneracy d is necessarily (d + 1)-biclique-free.Additionally, any nowhere dense family of graphs is biclique-free. More generally, if there exists an n-vertex graph that is not a 1-shallow minor of any graph in the family, then the family must be n-biclique-free, because all n-vertex graphs are 1-shallow minors of K n,n.

3. Dilworth's theorem - Wikipedia

   en.wikipedia.org/wiki/Dilworth's_theorem

   The complement of A forms a vertex cover in G with the same cardinality as this matching. This connection to bipartite matching allows the width of any partial order to be computed in polynomial time. More precisely, n-element partial orders of width k can be recognized in time O(kn 2). [3]

4. File:Minimum weight bipartite matching.pdf - Wikipedia

   en.wikipedia.org/wiki/File:Minimum_weight...

   You are free: to share – to copy, distribute and transmit the work; to remix – to adapt the work; Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses ...

5. Kőnig's theorem (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Kőnig's_theorem_(graph...

   Kőnig had announced in 1914 and published in 1916 the results that every regular bipartite graph has a perfect matching, [11] and more generally that the chromatic index of any bipartite graph (that is, the minimum number of matchings into which it can be partitioned) equals its maximum degree [12] – the latter statement is known as Kőnig's ...

6. Hall's marriage theorem - Wikipedia

   en.wikipedia.org/wiki/Hall's_marriage_theorem

   In the other direction, from any bipartite graph = (,,) one can define a finite family of sets, the family of neighborhoods of the vertices in , such that any system of unique representatives for this family corresponds to an -perfect matching in . In this way, the combinatorial formulation for finite families of finite sets and the graph ...

7. Matching polytope - Wikipedia

   en.wikipedia.org/wiki/Matching_polytope

   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 ...

8. Verizon settlement: Here's how much some customers are getting

   www.aol.com/verizon-settlement-payments...

   Verizon settlement payments have started hitting customers' bank accounts as part of a $100 million resolution of a class-action lawsuit.. Eligible customers had until April 15 to claim their ...

9. Inclusion–exclusion principle - Wikipedia

   en.wikipedia.org/wiki/Inclusion–exclusion...

   The inclusion exclusion principle forms the basis of algorithms for a number of NP-hard graph partitioning problems, such as graph coloring. [11] A well known application of the principle is the construction of the chromatic polynomial of a graph. [12]