Mar 9, 2020 · We prove for any finite poset P that sat(n,P)\le 2^{|P|-2}, a bound independent of the size n of the ground set. For induced copies of P, there ...
Our first main result proves that non-induced saturation numbers are always bounded by a function of , which is a constant independent of n.
Jul 26, 2022 · Our first main result proves that non-induced saturation numbers are always bounded by a function of |P|, which is a constant independent of n.
We say that a subfamily G⊆F of sets is ▶ a non-induced copy of P if there exists an injection i : P → G such that p ≤P q implies i(p) ⊂ i(q), ▶ an ...
Induced and non-induced poset saturation problems - NASA/ADS
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It turns out that if $P$ is given, processing the sets in this order and adding the sets greedily into our family whenever this does not ruin non-induced [ ...
Jul 2, 2021 · A subfamily G⊆F⊆2[n] G ⊆ F ⊆ 2 [ n ] of sets is a non-induced (weak) copy of a poset P in F F if there exists a bijection i:P→G i : P → G ...
Induced and non-induced poset saturation problems · Balázs Keszegh, N. Lemons, +2 authors. Balázs Patkós · Published in Journal of Combinatorial… 9 March 2020 ...
Apr 16, 2020 · We say that a family F of sets contains P if there exists an injection i : P → F such that p ≤P q implies i(p) ⊂ i(q). the poset ∨. Balázs ...
Saturation problems have been well studied in graph theory. A graph G is H-saturated if it does not contain a copy of the graph H, but adding any edge to G from ...
Recently, there has been an increasing interest in poset saturation problems, asking for the possible sizes of posets which are maximal with respect to the ...