New short proofs to some stability theorems
نویسندگان
چکیده
We present new short proofs to both the exact and stability result of two extremal problems. The first is about extension Turán’s theorem hypergraphs, second cancellative hypergraphs. Our are concise straightforward, but give a sharper version theorems
منابع مشابه
Short proofs of classical theorems
We give proofs of Ore’s theorem on Hamilton circuits, Brooks’ theorem on vertex coloring, and Vizing’s theorem on edge coloring, as well as the Chvátal-Lovász theorem on semi-kernels, a theorem of Lu on spanning arborescences of tournaments, and a theorem of Gutin on diameters of orientations of graphs. These proofs, while not radically different from existing ones, are perhaps simpler and more...
متن کاملStatistical Proofs of Some Matrix Theorems
Books on linear models and multivariate analysis generally include a chapter on matrix algebra, quite rightly so, as matrix results are used in the discussion of statistical methods in these areas. During recent years a number of papers have appeared where statistical results derived without the use of matrix theorems have been used to prove some matrix results which are used to generate other ...
متن کاملNew Proofs of (New) Direct Product Theorems
Direct product theorems are formal statements of the intuition, “It is harder to solve multiple instances of a problem than to solve a single instance.” For this talk, the amplification of hardness will be in reducing the probability of success for a feasible algorithm. So a direct product result for circuits might say, “If no small circuit can compute Boolean function f(x) with probability at ...
متن کاملNew Proofs of Euclid's and Euler's Theorems
In this note we give a new proof of the existence of infinitely many prime numbers. There are several different proofs with many variants, and some of them can be found in [1, 3, 4, 5, 6]. This proof is based on a simple counting argument using the inclusionexclusion principle combined with an explicit formula. A different proof based on counting arguments is due to Thue (1897) and can be found...
متن کاملNew Proofs of Basic Theorems in Calculus
In this note we present new proofs of three basic theorems in calculus. Although these theorems are well-known, in each proof we obtain something which seems to be unknown. We start with the Heine-Cantor theorem about uniform continuity and obtain explicitly the optimal delta for the given epsilon. We then proceed with the Weierstrass extreme value theorem and present two proofs of it: the “env...
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: European Journal of Combinatorics
سال: 2021
ISSN: ['1095-9971', '0195-6698']
DOI: https://doi.org/10.1016/j.ejc.2021.103350