The structure of large non-trivial <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e22" altimg="si3.svg"><mml:mi>t</mml:mi></mml:math>-intersecting families of finite sets

نویسندگان

چکیده

In this paper, we describe the structure of maximal non-trivial uniform t -intersecting families with large size for finite sets. special case when = 1 , our result gives rise to Kostochka and Mubayi’s in 2017.

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Weighted Non-Trivial Multiply Intersecting Families

Let n,r and t be positive integers. A family F of subsets of [n]={1,2, . . . ,n} is called r-wise t-intersecting if |F1∩·· ·∩Fr|≥ t holds for all F1, . . . ,Fr ∈F . An r-wise 1-intersecting family is also called an r-wise intersecting family for short. An r-wise t-intersecting family F is called non-trivial if |⋂F∈F F |<t. Let us define the Brace–Daykin structure as follows. F BD = {F ⊂ [n] : |...

متن کامل

Non-trivial intersecting uniform sub-families of hereditary families

For a family F of sets, let μ(F) denote the size of a smallest set in F that is not a subset of any other set in F , and for any positive integer r, let F (r) denote the family of r-element sets in F . We say that a family A is of Hilton-Milner (HM ) type if for some A ∈ A, all sets in A\{A} have a common element x / ∈ A and intersect A. We show that if a hereditary family H is compressed and μ...

متن کامل

Structure and properties of large intersecting families

We say that a family of k-subsets of an n-element set is intersecting, if any two of its sets intersect. In this paper we study different extremal properties of intersecting families, as well as the structure of large intersecting families. We also give some results on k-uniform families without s pairwise disjoint sets, related to Erdős Matching Conjecture. We prove a conclusive version of Fra...

متن کامل

Maximal Intersecting Families of Finite Sets and «uniform Hjelmslev Planes

The following theorem is proved. The collection of lines of an n-uniform projective Hjelmslev plane is maximal when considered as a collectiion of mutually intersecting sets of equal cardinality.

متن کامل

Multiply intersecting families of sets

Let [n] denote the set {1, 2, ..., n}, 2 the collection of all subsets of [n] and F ⊂ 2 be a family. The maximum of |F| is studied if any r subsets have an at least s-element intersection and there are no ` subsets containing t+1 common elements. We show that |F| ≤ Pt−s i=0 n−s i + t+`−s t+2−s n−s t+1−s + `− 2 and this bound is asymptotically the best possible as n →∞ and t ≥ 2s ≥ 2, r, ` ≥ 2 a...

متن کامل

ذخیره 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.2021.103373