Given a family of (hyper) graphs $\mathcal {F} $ a (hyper) graph $ G $ is said to be $\mathcal
{F} $-saturated if $ G $ is $ F $-free for any $ F\in\mathcal {F} $ but for any edge e in the …

Saturation problems for forbidden graphs have been a popular area of research for many
decades, and recently Brualdi and Cao initiated the study of a saturation problem for 0-1 …

A 0-1 matrix M is saturating for a 0-1 matrix P if M does not contain a submatrix that can be
turned into P by changing some 1 entries to 0 entries, and changing an arbitrary 0 to 1 in M …

In this paper, we introduce saturation and semisaturation functions of sequences, and we
prove a number of fundamental results about these functions. Given a forbidden sequence u …

For n> 2 k≥ 4 we consider intersecting families F consisting of k-subsets of {1, 2,…, n}. Let I
(F) denote the family of all distinct intersections F∩ F′, F≠ F′ and F, F′∈ F. Let A consist …

In this paper, we introduce saturation and semisaturation functions of sequences, and we
prove a number of fundamental results about these functions. Given a forbidden sequence u …

Recently, the saturation problem of 0-1 matrices has gained a lot of attention. This problem
can be regarded as a saturation problem of ordered bipartite graphs. Motivated by this, we …

A family $\mathcal {F} $ on ground set $[n]:=\{1, 2,\ldots, n\} $ is maximal $ k $-wise
intersecting if every collection of at most $ k $ sets in $\mathcal {F} $ has non-empty …

A family F on ground set [n]:={1, 2,…, n} is maximal k-wise intersecting if every collection of
at most k sets in F has non-empty intersection, and no other set can be added to F while …

Given natural numbers $ k\leq s\leq n $, we ask: what is the minimal VC-dimension of a
family $\mathcal {F} $ of $ s $-subsets of $[n] $ that covers all $ k $-subsets of $[n] $? We first …