Turan’s Theorem 1 Introduction Extremal graph theory is the branch of graph theory that studies extremal (maximal or minimal) graphs which satisfy a certain property. Extremality can be taken with respect to di erent graph invariants, such as order, …
Turán's Theorem -- from Wolfram MathWorld
2024年10月10日 · Let G (V,E) be a graph with graph vertices V and graph edges E on n graph vertices without a (k+1)-clique. Then t (n,k)<= ( (k-1)n^2)/ (2k), where t (n,k) is the edge count.
A note on Turán’s theorem - ScienceDirect
2019年11月15日 · Turán’s theorem is a cornerstone of the extremal graph theory. In this paper, we determine the minimum number of edges of a connected graph without containing an independent vertex set of a given size and give a new proof of Turán’s theorem.
Turan's Graph Theorem. One of the fundamental results in graph theory is the Theorem of Turan, proved in 1941, which initiated extremal graph theory. (See the book [2] by Bollobas as a standard reference.)
Turan’s theorem K r+1 = complete graph of order r + 1 Tur an graph T r(n): complete r-partite graph with equal parts. t r(n) = e(T r(n)) = r 1 2r n 2 + O(r) Theorem: (Tur an 1941, Mantel 1907 for r = 2) For all r 2, the unique largest K r+1-free graph on n vertices is T r(n).
Theorem: (Keevash and S., Erdos et al. for r = 2) There exists r > 0 such that if G is a K r+1-free graph of order n and 1− r ≤α ≤1, then G contains a subset of size αn which spans at most r −1 2r (2α −1)n2 edges. Equality is attained only by the Tur´an graph T r(n).
combinatorics - Deriving the number of edges in a Turán graph ...
2015年3月31日 · When stating Turán's theorem, the Turán graphs are often used to give an upper bound on the possible number of edges in a graph without a clique of a certain size. This bound can also be proven explicitly (see this for different ways to state/prove the theorem).
1 Introduction. One of the classical theorems in graph theory is Turan's Theorem which states that a graph on n vertices. t (1 1=t + o(1)) n edges. Sudakov, S. 2. ation of Turan's Theorem. A graph G is said to be t-Turan if any s. the number of edges.
Turán’s Graph Theorem [2] states that any undirected, simple graph with n vertices that does not contain a p-clique, contains at most 1. p. n2. 2 edges. The theorem is an important result in graph theory and the foundation of the field of extremal graph theory.
Turán’s graph theorem Chapter 41 Paul Turán One of the fundamental results in graph theory is the theorem of Turán from 1941, which initiated extremal graph theory. Turán’s theorem was rediscovered many times with various different proofs. We will discuss five of them and let the reader decide which one belongs in The Book.
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