König's Theorem (set Theory)
There are several theorems associated with the name König or Kőnig: * König's theorem (set theory), named after the Hungarian mathematician Gyula Kőnig. * König's theorem (complex analysis), named after the Hungarian mathematician Gyula Kőnig. * Kőnig's theorem (graph theory), named after his son Dénes Kőnig. * König's theorem (kinetics), named after the German mathematician Samuel König. See also * Kőnig's lemma (also known as Kőnig's infinity lemma), named after Dénes Kőnig {{mathdab ...
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König's Theorem (complex Analysis)
In complex analysis and numerical analysis, König's theorem, named after the Hungarian mathematician Gyula Kőnig, gives a way to estimate simple poles or simple roots of a function. In particular, it has numerous applications in root finding algorithms like Newton's method and its generalization Householder's method. Statement Given a meromorphic function In the mathematical field of complex analysis, a meromorphic function on an open subset ''D'' of the complex plane is a function that is holomorphic on all of ''D'' ''except'' for a set of isolated points, which are ''poles'' of the function. ... defined on , x, : :$f(x)\; =\; \backslash sum\_^\backslash infty\; c\_nx^n,\; \backslash qquad\; c\_0\backslash neq\; 0.$ which only has one simple pole $x=r$ in this disk. Then :$\backslash frac\; =\; r\; +\; o(\backslash sigma^),$ where such that . In particular, we have :$\backslash lim\_\; \backslash frac\; =\; r.$

Intuition

Recall that :$\backslash frac=-\backslash frac\backslash \; ...$
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Kőnig's Theorem (graph Theory)
In the mathematics, mathematical area of graph theory, Kőnig's theorem, proved by , describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs. It was discovered independently, also in 1931, by Jenő Egerváry in the more general case of weighted graphs. Setting A vertex cover in a graph is a set of vertices that includes at least one endpoint of every edge, and a vertex cover is ''minimum'' if no other vertex cover has fewer vertices. A matching (graph theory), matching in a graph is a set of edges no two of which share an endpoint, and a matching is ''maximum'' if no other matching has more edges. It is obvious from the definition that any vertex-cover set must be at least as large as any matching set (since for every edge in the matching, at least one vertex is needed in the cover). In particular, the minimum vertex cover set is at least as large as the maximum matching set. Kőnig's theorem states that, in any bip ...
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König's Theorem (kinetics)
There are several theorems associated with the name König or Kőnig: * König's theorem (set theory), named after the Hungarian mathematician Gyula Kőnig. * König's theorem (complex analysis), named after the Hungarian mathematician Gyula Kőnig. * Kőnig's theorem (graph theory), named after his son Dénes Kőnig. * König's theorem (kinetics), named after the German mathematician Samuel König. See also * Kőnig's lemma Kőnig's lemma or Kőnig's infinity lemma is a theorem in graph theory due to the Hungarian mathematician Dénes Kőnig who published it in 1927. It gives a sufficient condition for an infinite graph to have an infinitely long path. The computab ...