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We prove that, for any $tge 3$, there exists a constant $c=c(t)>0$ such that any $d$-regular $n$-vertex graph with the second largest eigenvalue in absolute value~$lambda$ satisfying $lambdale c d^{t-1}/n^{t-2}$ contains vertex-disjoint copies of $K_t$ covering all but at most $n^{1-1/(8t^4)}$ vertices. This provides further support for the conjecture of Krivelevich, Sudakov and Szabo [emph{Triangle factors in sparse pseudo-random graphs}, Combinatorica textbf{24} (2004), pp.~403--426] that $(n,d,lambda)$-graphs with $nin 3mathbb{N}$ and $lambdaleq cd^{2}/n$ for a suitably small absolute constant~$c>0$ contain triangle-factors.
We prove that for any $tge 3$ there exist constants $c>0$ and $n_0$ such that any $d$-regular $n$-vertex graph $G$ with $tmid ngeq n_0$ and second largest eigenvalue in absolute value $lambda$ satisfying $lambdale c d^{t}/n^{t-1}$ contains a $K_t$-fa
We consider extremal problems for subgraphs of pseudorandom graphs. For graphs $F$ and $Gamma$ the generalized Turan density $pi_F(Gamma)$ denotes the density of a maximum subgraph of $Gamma$, which contains no copy of~$F$. Extending classical Turan
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 $G$, i.e. an embedding $varphicolon V(H)to V(G)$ so that $varphi(u)varphi(v)in E(G)$ for all $uvin E(H)$. Particu
We study the appearance of powers of Hamilton cycles in pseudorandom graphs, using the following comparatively weak pseudorandomness notion. A graph $G$ is $(varepsilon,p,k,ell)$-pseudorandom if for all disjoint $X$ and $Ysubset V(G)$ with $|X|gevare
We establish a so-called counting lemma that allows embeddings of certain linear uniform hypergraphs into sparse pseudorandom hypergraphs, generalizing a result for graphs [Embedding graphs with bounded degree in sparse pseudorandom graphs, Israel J.