Notes on a classic theorem of Erdős and Grünwald
نویسندگان
چکیده
منابع مشابه
Lecture 4 : Turán ’ s theorem and Erdős - Stone theorem
The lower bound is the same as before, due to the fact that Tr(n) is Kr+1-free. Define the adjacency matrix A = A(G) = (aij) for a graph G of order n. Let V = {v1, · · · , vn}. Then A is a n-by-n 0 − 1 matrix such that aij = 1 if and only if vivj ∈ E. Thus A is symmetric. We will be interested in a quadratic form ⟨Ax,x⟩ where x denotes a vector of length n. This is often called the Lagrangian o...
متن کاملSperner's Theorem and a Problem of Erdős, Katona and Kleitman
A central result in extremal set theory is the celebrated theorem of Sperner from 1928, which gives the size of the largest family of subsets of [n] not containing a 2-chain F1 ⊂ F2. Erdős extended this theorem to determine the largest family without a k-chain F1 ⊂ F2 ⊂ . . . ⊂ Fk. Erdős and Katona, followed by Kleitman, asked how many chains must appear in families with sizes larger than the c...
متن کاملOn the stability of the Erdős-Ko-Rado theorem
Delete the edges of a Kneser graph independently of each other with some probability: for what probabilities is the independence number of this random graph equal to the independence number of the Kneser graph itself? We prove a sharp threshold result for this question in certain regimes. Since an independent set in the Kneser graph is the same as a uniform intersecting family, this gives us a ...
متن کاملNotes on Freiman’s Theorem
Freiman’s Theorem describes the structure of a set A under the condition that A+ A has size close to that of A. If P is a generalized arithmetic progression, then |P +P | is close to |P |. Freiman’s Theorem states the partial converse: if |P + P | is close to P then P must be contained in a small generalized arithmetic progression. The theorem may be stated as follows, and we will give the rema...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2011
ISSN: 0021-9045
DOI: 10.1016/j.jat.2011.02.008