Apr 7, 2017 · For k=2 and 3, the conjecture is true, but for larger values of k the best known upper bound, due to Lomonosov, is |\mathcal{F}|=O_{k}(n\log n).
Apr 7, 2017 · We say that a family F ⊂ 2[n] is k-cross-free if it does not contain k pairwise crossing sets. The following conjecture was made by Karzanov and ...
On the Size of K-Cross-Free Families | Combinatorica - SpringerLink
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Feb 7, 2018 · Two subsets A,B of an n-element ground set X are said to be crossing, if none of the four sets A∩B, A\B, B\A and X\(A∪B) are empty.
It was conjectured by Karzanov and Lomonosov forty years ago that if a family F of subsets of X does not contain k pairwise crossing elements, then |F|=O(kn).
We say that a family F ⊂ 2[n] is k-cross-free if it does not contain k pairwise crossing sets. The following conjecture was made by Karzanov and. Lomonosov [15] ...
We give a short and simple proof for the theorem that the size of a 3-cross-free family is linear in the size of the groundset. A family is 3-cross-free if it ...
Two subsets A,B of an n-element ground set X are said to be crossing, if none of the four sets A?B, A\B, B\A and X\(A?B) are empty.
Apr 7, 2017 · For $k=2$ and $3$, the conjecture is true, but for larger values of $k$ the best known upper bound, due to Lomonosov, is $|\mathcal{F}|=O_{k}(n\ ...
Aug 16, 2018 · Abstract. Two subsets A,B of an n-element ground set X are said to be crossing, if none of the four sets A∩B, A\B, B\A and X\(A∪B) are empty ...
We give a short and simple proof for the theorem that the size of a 3-cross-free family is linear in the size of the groundset. A family is 3-cross-free if it ...