A perfect K r‐tiling in a graph G is a collection of vertex‐disjoint copies of K r that together
cover all the vertices in G. In this paper we consider perfect K r‐tilings in the setting of …

For ak k‐vertex graph FF and an nn‐vertex graph GG, an FF‐tiling in GG is a collection of
vertex‐disjoint copies of FF in G G. For r∈ ℕ r ∈ N, the rr‐independence number of GG …

We prove that, for any t≥ 3, there exists a constant c= c (t)> 0 such that any d-regular n-
vertex graph with the second largest eigenvalue in absolute value λ satisfying λ≤ cdt− 1/nt …

We investigate the emergence of subgraphs in sparse pseudo‐random k‐uniform
hypergraphs, using the following comparatively weak notion of pseudo‐randomness. A k …

Given an n‐vertex pseudorandom graph G and an n‐vertex graph H with maximum degree
at most two, we wish to find a copy of H in G, that is, an embedding φ: V (H)→ V (G) so that φ …

An (n, d, λ)-graph is an n vertex, d-regular graph with second eigenvalue in absolute value λ.
When λ is small compared to d, such graphs have pseudorandom properties and make …

We prove that, for any for a suitably small absolute constant c> 0 contain triangle-factors. Our
arguments combine tools from linear programming with probabilistic techniques, and apply …

For a $ k $-vertex graph $ F $ and an $ n $-vertex graph $ G $, an $ F $-tiling in $ G $ is a
collection of vertex-disjoint copies of $ F $ in $ G $. For $ r\in\mathbb {N} $, the $ r …

An n-vertex graph is said to to be. p; ˇ/-bijumbled if for any vertex sets A; B Â VG/, we have
eA; B/D pjAjjBj ˇpjAjjBj: We prove that for any r 2 N 3 and c> 0 there exists an"> 0 such that …

Clique Factors: Extremal and Probabilistic Perspectives Page 1 Clique Factors: Extremal and
Probabilistic Perspectives w1 w2 w3 w4 Dissertation zur Erlangung des Grades eines Doktors …