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MathematicalPhysicist
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did someone proove this conjecture or is still just a conjecture?
where can i find the proof?Originally posted by selfAdjoint
According to a google search one Alan Swett says he has proved it for all n < 10^14. I can't verify the proof.
The Erdos-Strauss Conjecture is a mathematical conjecture proposed by mathematicians Paul Erdos and Ernst Gabor Strauss in the 1940s. It states that for any positive integer k, there exists a finite number g(k) such that every graph with more than g(k) vertices and no clique of size k has a chromatic number of at most k-1. In simpler terms, it suggests that for any given number of colors, there is a maximum number of vertices in a graph that can be colored without creating a clique of a certain size.
No, the Erdos-Strauss Conjecture has not been proven. It remains an open problem in mathematics and has been extensively studied by mathematicians for decades. While some progress has been made and special cases have been proven, the general conjecture still remains unsolved.
The Erdos-Strauss Conjecture is important because it has connections to various fields of mathematics, including graph theory, combinatorics, and number theory. It has also sparked interest in the study of chromatic numbers and the structure of graphs. Additionally, if proven to be true, it would have important implications in the study of coloring problems and could potentially lead to new mathematical discoveries.
No, there are currently no known counterexamples to the Erdos-Strauss Conjecture. However, as it has not been proven, it is possible that a counterexample may exist. In fact, one of the main challenges in proving the conjecture is to find a counterexample or to prove that one does not exist.
While there are currently no direct applications of the Erdos-Strauss Conjecture, its study has led to developments in other areas of mathematics and computer science. For example, it has been used to study Ramsey numbers, which have applications in scheduling problems and communication networks. Additionally, the techniques and methods used in attempting to prove the conjecture have led to new insights and results in graph theory and combinatorial optimization.