Oliver Cooley

Publications40
h-index8
Citations251
Highly Influential Citations20
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Tight cycles and regular slices in dense hypergraphs
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Embeddings and Ramsey numbers of sparse κ-uniform hypergraphs
TLDR
The main new tool which is proved and used is an embedding lemma for κ-uniform hypergraphs of bounded maximum degree into suitable δ- uniform ‘quasi-random’hypergraphs.
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Proof of the Loebl-Komlós-Sós conjecture for large, dense graphs
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The minimum vertex degree for an almost-spanning tight cycle in a 3-uniform hypergraph
View PDF on arXiv
Large Induced Matchings in Random Graphs
TLDR
This paper proves an asymptotically best possible result for induced matchings by showing that if G(n,p) contains an induced matching of order approximately $2\log_q(np)$, where $q= \frac{1}{1-p}$.
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Perfect packings with complete graphs minus an edge
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Subcritical random hypergraphs, high-order components, and hypertrees
TLDR
One of the central topics in the theory of random graphs deals with the phase transition in the order of the largest components, in the binomial random graph $\mathcal{G}(n,p)$, where n is the number of particles in the graph.
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3-Uniform hypergraphs of bounded degree have linear Ramsey numbers
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Threshold and Hitting Time for High-Order Connectedness in Random Hypergraphs
TLDR
A hitting time result is deduced for the random hypergraph process –  the hypergraph becomes $j-connected at exactly the moment when the last isolated $j$-set disappears.
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Largest Components in Random Hypergraphs
TLDR
It is shown that the existence of a j-tuple-connected component containing Θ(nj) j-sets undergoes a phase transition and the threshold occurs at edge probability, which controls the structure of the component grown in the search process.
View on Cambridge Press
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