In graph theory, Turán's theorem bounds the number of edges that can be included in an undirected graph that does not have a complete subgraph of a given...

Erdős–Stone theorem extends Turán's theorem by bounding the number of edges in a graph that does not have a fixed Turán graph as a subgraph. Via this theorem, similar...

Ramsey-Turán theory is a subfield of extremal graph theory. It studies common generalizations of Ramsey's theorem and Turán's theorem. In brief, Ramsey-Turán...

for G = K r {\displaystyle G=K_{r}} . Equality cases for Turán's theorem come from the Turán graph T ( n , r − 1 ) {\displaystyle T(n,r-1)} . This result...

more briefly today as extremal graph theory. Turán's best-known result in this area is Turán's graph theorem, that gives an upper bound on the number of...

demonstrates the use of pessimistic estimators. One way of stating Turán's theorem is the following: Any graph G = (V, E) contains an independent set...

In extremal graph theory, the Erdős–Stone theorem is an asymptotic result generalising Turán's theorem to bound the number of edges in an H-free graph...

or Turán-type result, after Turán's theorem. Notable examples include Szemerédi's theorem, which is such a strengthening of van der Waerden's theorem, and...

In mathematics, Turán's method provides lower bounds for exponential sums and complex power sums. The method has been applied to problems in equidistribution...

families of graphs defined by forbidden subgraphs of various types Turán's theorem, a bound on the number of edges of a graph with a forbidden complete...

Mantel's Theorem (1907) and Turán's Theorem (1941) were some of the first milestones in the study of extremal graph theory. In particular, Turán's theorem would...

Moon–Moser graphs K3,3,..., a special case of the Turán graphs arising as the extremal cases in Turán's theorem. Hadwiger's conjecture, still unproven, relates...

(Ramsey theory) Tutte theorem (graph theory) Turán's theorem (graph theory) Van der Waerden's theorem (combinatorics) Wagner's theorem (graph theory) Zeilberger–Bressoud...

Mantel's theorem. Mantel's result was generalized to k-partite graphs and graphs that avoid larger cliques as subgraphs in Turán's theorem, and these...

graphs with no induced 3-cycle, or locally independent graphs. By Turán's theorem, the n-vertex triangle-free graph with the maximum number of edges...

density of triangles to the density of edges. A classic example is Turán's Theorem, which states that if t ( K r , W ) = 0 {\displaystyle t(K_{r},W)=0}...

k^{2}-3k/2} if k {\displaystyle k} is even. These bounds generalize Turán's theorem on the number of edges in a triangle-free graph, and they are the best...

art gallery theorem Five proofs of Turán's theorem Shannon capacity and Lovász number Chromatic number of Kneser graphs Friendship theorem Some proofs...

features depend on other parameters of the input. For example, consider Turán's theorem, which can be stated as "any graph with n {\displaystyle n} vertices...

exposition of Turán's proof in Hardy & Wright, §22.11. Tenenbaum: 305–308  gives a proof of the Hardy–Ramanujan theorem using the Turán–Kubilius inequality...

dominating set Extremal graph theory Critical graph Turán's theorem Frequency partition Frucht's theorem Girth Graph drawing Graph homomorphism Graph labeling...

In mathematics, the Erdős–Turán inequality bounds the distance between a probability measure on the circle and the Lebesgue measure, in terms of Fourier...

combinatorics, Szemerédi's theorem is a result concerning arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured that every...

called null graph. Turán 1.  Pál Turán 2.  A Turán graph is a balanced complete multipartite graph. 3.  Turán's theorem states that Turán graphs have the...

given class of forbidden subgraphs? The prototype of such results is Turán's theorem, where there is one forbidden subgraph: a complete graph with k vertices...

awarded the Széchenyi Prize. One of her contributions is the Kővári–Sós–Turán theorem concerning the maximum possible number of edges in a bipartite graph...

bipartite graphs, and the even circuit theorem for this case can be seen as a special case of the Kővári–Sós–Turán theorem. More precisely, in this case it...

a modified version of Turán's result allows one to prove the Hardy–Ramanujan Theorem with any even moment. Almost prime Turán–Kubilius inequality Hardy...

ISSN 0012-365X. Bellmann, Louis; Reiher, Christian (2019-10-02). "Turán's Theorem for the Fano Plane". Combinatorica. 39 (5): 961–982. arXiv:1804.07673...

most 2 m {\displaystyle 2{\sqrt {m}}} neighbors; for otherwise by Turán's theorem the neighbors of the vertex would not have enough remaining edges to...