Olaf Parczyk
Technische Universität Ilmenau
47 Papers
112 Citations
Olaf Parczyk is an academic researcher from Technische Universität Ilmenau. The author has contributed to research in topics: Random graph & Hypergraph. The author has an hindex of 8, co-authored 44 publications. Previous affiliations of Olaf Parczyk include London School of Economics and Political Science & Goethe University Frankfurt.
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Papers
Embedding spanning bounded degree graphs in randomly perturbed graphs
TL;DR: For the model G 8 G(n; p) of randomly perturbed dense graphs, where G is any n-vertex graph with minimum degree at least n and G is the binomial random graph as discussed by the authors, it is shown that if p =!(n−2~(+1)) then G 8 g(n, p) with high probability contains a copy of F. The bound used for p here is lower by a log-factor in comparison to the conjectured threshold for the general appearance of such subgraphs in G (n,p)
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Universality for bounded degree spanning trees in randomly perturbed graphs
TL;DR: In this paper, the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs has been solved, and it is shown that with high probability the graph Gα∪G(n,C/n) contains copies of all spanning trees with maximum degree at most Δ simultaneously, where C depends only on α and Δ.
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Universality for bounded degree spanning trees in randomly perturbed graphs
TL;DR: It is shown that with high probability the graph Gα∪G(n,C/n) contains copies of all spanning trees with maximum degree at most Δ simultaneously, where C depends only on α and Δ.
Spanning structures and universality in sparse hypergraphs
Olaf Parczyk,Yury Person +1 more
TL;DR: It is shown that the random graph G(n, p) for appropriate p and explicit constructions of universal graphs due to Alon, Capalbo, Kohayakawa, Rödl, Ruciński and Szemerédi yield constructions that are sparser than the random hypergraph H(r)(n,p) with p≫(lnn/n)1/Δ © 2016 Wiley Periodicals, Inc.
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Embedding spanning bounded degree graphs in randomly perturbed graphs
TL;DR: In this article, the authors studied the appearance of spanning subgraphs in randomly perturbed dense graphs, and showed that the appearance threshold of a Hamilton cycle with high probability appears in G(n,p) when p=\omega(n^{-2/(\Delta+1)}).
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