What does FKN mean in UNCLASSIFIED
The FKN theorem is a result in Ramsey theory that states that for any positive integer r, there exists a positive integer N(r) such that for any n ≥ N(r) and any n-vertex graph, there exists either a set of r vertices that are all connected or a set of r vertices that are all disconnected.
FKN meaning in Unclassified in Miscellaneous
FKN mostly used in an acronym Unclassified in Category Miscellaneous that means Friedgut Kalai Naor
Shorthand: FKN,
Full Form: Friedgut Kalai Naor
For more information of "Friedgut Kalai Naor", see the section below.
- FKN stands for Friedgut Kalai Naor, named after its three creators: Ehud Friedgut, Gil Kalai, and Assaf Naor.
Meaning and Usage
- FKN is a concept in mathematics, specifically in the field of extremal combinatorics.
- It refers to a theorem that provides a lower bound on the number of edges in a graph with given properties.
- The theorem states that for a graph with n vertices and degree sequence d1, d2, ..., dn, the number of edges is at least (1/2) * (Σ(di)^2 / Σ(di + 1)).
- This theorem has applications in various areas, such as graph theory, Ramsey theory, and coding theory.
Essential Questions and Answers on Friedgut Kalai Naor in "MISCELLANEOUS»UNFILED"
What is the Friedgut-Kalai-Naor (FKN) theorem?
What is the significance of the FKN theorem?
The FKN theorem is a fundamental result in Ramsey theory, and it has applications in various areas of mathematics, including graph theory, combinatorics, and number theory. For example, it can be used to prove the Erdős-Szekeres theorem, which states that for any positive integers r and s, there exists a positive integer N(r, s) such that any set of N(r, s) points in the plane in general position contains either r points that are all collinear or s points that are all affinely independent.
How is the FKN theorem proved?
The FKN theorem can be proved using a variety of techniques, including topological methods and probabilistic arguments. One common approach is to use the probabilistic method, which involves showing that the probability of a random graph satisfying the desired property is greater than 0.
What are some generalizations of the FKN theorem?
There are several generalizations of the FKN theorem. For example, one can consider the case where the graph is not necessarily complete, or the case where the sets of vertices that are all connected or all disconnected are required to have certain additional properties.
Final Words:
- FKN is an important theorem in extremal combinatorics that establishes a lower bound on the number of edges in a graph.
- It is widely used in various mathematical disciplines and provides insights into the structure and properties of graphs.
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