• Publications
  • Influence
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.
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 $q= \frac{1}{1-p}$.
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.
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.
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.
...
...