A bound for 1-cross intersecting set pair systems
نویسندگان
چکیده
A well-known result of Bollobás says that if { ( i , B ) } = 1 m is a set pair system such | ? and b for ? j ? 0? only then + . Füredi, Gyárfás Király recently initiated the study systems with additional property all Confirming conjecture theirs, we show this extra condition allows an improvement upper bound (at least) by constant factor.
منابع مشابه
Union-Intersecting Set Systems
Three intersection theorems are proved. First, we determine the size of the largest set system, where the system of the pairwise unions is l-intersecting. Then we investigate set systems where the union of any s sets intersect the union of any t sets. The maximal size of such a set system is determined exactly if s + t ≤ 4, and asymptotically if s + t ≥ 5. Finally, we exactly determine the maxi...
متن کاملOn Cross-Intersecting Families of Set Partitions
Let B(n) denote the collection of all set partitions of [n]. Suppose A1,A2 ⊆ B(n) are cross-intersecting i.e. for all A1 ∈ A1 and A2 ∈ A2, we have A1 ∩A2 6= ∅. It is proved that for sufficiently large n,
متن کاملA Generic Set That Does Not Bound a Minimal Pair
The structure of the semi lattice of enumeration degrees has been investigated from many aspects. One aspect is the bounding and nonbounding properties of generic degrees. Copestake proved that every 2-generic enumeration degree bounds a minimal pair and conjectured that there exists a 1-generic set that does not bound a minimal pair. In this paper we verify this longstanding conjecture by cons...
متن کاملIntersecting set systems and graphic matroids,
Two simple proofs are given to an earlier partial result about an extremal set theoretic conjecture of Chung, Frank!, Graham, Shearer and Faudree, Schelp, S6s, respectively. The statement is slightly strengthened within a matroid theoretic framework. The first proof re lies on results from matroid theory, while the second is based on an explicit constJuction providing an elementary proof. @ 199...
متن کاملOn Families of Weakly Cross-intersecting Set-pairs
Let F be a family of pairs of sets. We call it an (a, b)-set system if for every set-pair (A,B) in F we have that |A| = a, |B| = b, A ∩ B = ∅. The following classical result on families of cross-intersecting set-pairs is due to Bollobás [6]. Let F be an (a, b)-set system with the cross-intersecting property, i.e., for (Ai, Bi), (Aj, Bj) ∈ F with i 6= j we have that both Ai ∩ Bj and Aj ∩ Bi are ...
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.2021.103345