Extremal Finite Set Theory surveys old and new results in the area of extremal set system
theory. It presents an overview of the main techniques and tools (shifting, the cycle method …

Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and
eigenvectors of matrices associated with graphs to study them. In this paper, we present a …

The notion of weak saturation was introduced by Bollobás in 1968. Let F and H be graphs. A
spanning subgraph G⊆ F is weakly (F, H)-saturated if it contains no copy of H but there …

A graph G is called H‐saturated if it does not contain any copy of H, but for any edge e in the
complement of G, the graph contains some H. The minimum size of an n‐vertex H‐saturated …

ABSTRACT A graph H is Ks‐saturated if it is a maximal Ks‐free graph, ie, H contains no
clique on s vertices, but the addition of any missing edge creates one. The minimum number …

Given a poset P, a family F of elements in the Boolean lattice is said to be P-saturated if (1) F
contains no copy of P as a subposet and (2) every proper superset of F contains a copy of P …

A graph G is called F-saturated if G does not contain F as a subgraph (not necessarily
induced) but the addition of any missing edge to G creates a copy of F. The saturation …

For a fixed poset $ P $, a family $\mathcal F $ of subsets of $[n] $ is induced $ P $-saturated
if $\mathcal F $ does not contain an induced copy of $ P $, but for every subset $ S $ of $[n] …

For given graphs G and H, the graph G is H-saturated if G does not contain H as a subgraph
but for any e∈ E (G‾), G+ e contains H. In this note, we prove that if G is an n-vertex K r+ 1 …

For two graphs G and F, we say that G is weakly F-saturated if G has no copy of F as a
subgraph and one can join all the nonadjacent pairs of vertices of G in some order so that a …