An r -wise t -intersecting family F is maximal if adding another k -element subset to F will lose r -wise t -intersecting property. In k -uniform intersecting ...

2022/07/29 · In this paper, we prove that if n \gs n_0(r, t, k) , then the r -wise t -intersecting family \CF \subseteq \binom{[n]}{k} containing the most (r ...

In this paper, we prove that if n ⩾ n 0 ( r , t , k ) , then the r -wise t -intersecting family F ⊆ [ n ] k containing the most ( r + 1 , t ) -triangles is ...

2023/08/01 · In this paper, we prove that if n ⩾ n 0 ( r, t, k ), then the r-wise t-intersecting family F ⊆ [ n ] k containing the most ( r + 1, t )- ...

Our main result is a construction of four families C_1,C_2,B_1,B_2 which are equipollent with the power set of the real line R and satisfy the following ...

Let $t$, $r$, $k$ and $n$ be positive integers and $\mathcal{F}$ a family of $k$-subsets of an $n$-set $V$. The family $ \CF $ is $ r $-wise $ t ...

2022/07/29 · An r -wise t -intersecting family of r + 1 sets { T 1 , … , T r + 1 } is called an ( r + 1 , t ) -triangle if | T 1 ∩ ⋯ ∩ T r + 1 | \ls t − 1 .

We conjecture that every 4-wise intersecting clutter is non-ideal. As evidence for our conjecture, we prove it in the binary case. Two key ingredients for our ...

2022/01/07 · A family \mathcal{F} of sets is r-wise intersecting if for any F_1,F_2,\dots,F_r\in \mathcal{F} we have \cap_{i=1}^rF_i\neq \emptyset or ...

2022/08/22 · A family of sets is r-wise intersecting if for any we have or equivalently if does not contain any m-triangle for .