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 …

In a graph $ G $, a geodesic between two vertices $ x $ and $ y $ is a shortest path
connecting $ x $ to $ y $. A subset $ S $ of the vertices of $ G $ is in general position if no …

Let F be a set system on n with all sets having k elements and every pair of sets intersecting.
The celebrated theorem of Erdős, Ko and Rado from 1961 says that, provided n≥ 2 k, any …

For integers $ n\geq k\geq 1$, the {\em Kneser graph} $ K (n, k) $ is the graph with vertex-set
consisting of all the $ k $-element subsets of $\{1, 2,\ldots, n\} $, where two $ k $-element …

Let V be an n-dimensional vector space over the finite field F q and let V kq denote the family
of all k-dimensional subspaces of V. A family F⊆ V kq is called intersecting if for all F, F′∈ …

Let $ V $ be a finite dimensional vector space over a finite field, and $\mathcal {F} $ a family
consisting of $ k $-subspaces of $ V $. The family $\mathcal {F} $ is called $ t $-intersecting if …

Treewidth is an important and well-known graph parameter that measures the complexity of
a graph. The Kneser graph Kneser (n, k) is the graph with vertex set $\binom {[n]}{k} $, such …

The Kneser cube $ Kn_n $ has vertex set $2^{[n]} $ and two vertices $ F, F'$ are joined by
an edge if and only if $ F\cap F'=\emptyset $. For a fixed graph $ G $, we are interested in the …

Both treewidth and the Hadwiger number are key graph parameters in structural and
algorithmic graph theory, especially in the theory of graph minors. For example, treewidth …

The Kneser graph KG n, k is a graph whose vertex set is the family of all k-subsets of [n] and
two vertices are adjacent if their corresponding subsets are disjoint. The classical Erdős–Ko …