Large Induced Matchings in Random Graphs

Autor: Oliver Cooley, Nemanja Draganić, Benny Sudakov, Mihyun Kang

Publikováno v: SIAM Journal on Discrete Mathematics, 35 (1)

Given a large graph H, does the binomial random graph G(n, p) contain a copy of H as an induced subgraph with high probability? This classical question has been studied extensively for various graphs H, going back to the study of the independence num

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cd74e33b66d22108602072d8e7437e7b
https://doi.org/10.1137/20m1330609

Vanishing of cohomology groups of random simplicial complexes

Autor: Oliver Cooley, Nicola Del Giudice, Philipp Sprüssel, Mihyun Kang

Publikováno v: Random Structures & Algorithms. 56:461-500

We consider $k$-dimensional random simplicial complexes that are generated from the binomial random $(k+1)$-uniform hypergraph by taking the downward-closure, where $k\geq 2$. For each $1\leq j \leq k-1$, we determine when all cohomology groups with

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d5b2d4a658f95fc8d004abc97b3316fc
https://doi.org/10.1002/rsa.20857

Subcritical Random Hypergraphs, High-Order Components, and Hypertrees

Autor: Oliver Cooley, Wenjie Fang, Mihyun Kang, Nicola Del Giudice

Publikováno v: SIAM Journal on Discrete Mathematics
SIAM Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2020, 34 (4), pp.2033-2062. ⟨10.1137/18M1221527⟩
Scopus-Elsevier
ANALCO

In the binomial random graph $\mathcal{G}(n,p)$, when $p$ changes from $(1-\varepsilon)/n$ (subcritical case) to $1/n$ and then to $(1+\varepsilon)/n$ (supercritical case) for $\varepsilon>0$, with high probability the order of the largest component

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9f2dfac3f85aa12fde45d725cf684b30
https://hal.archives-ouvertes.fr/hal-03112278

Jigsaw percolation on random hypergraphs

Autor: Béla Bollobás, Christoph Koch, Mihyun Kang, Oliver Cooley

Publikováno v: Journal of Applied Probability. 54:1261-1277

The jigsaw percolation process on graphs was introduced by Brummittet al.(2015) as a model of collaborative solutions of puzzles in social networks. Percolation in this process may be viewed as the joint connectedness of two graphs on a common vertex

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1e541bb669396149eb6bce6419bf7cb9
https://doi.org/10.1017/jpr.2017.62

How does the core sit inside the mantle?

Autor: Kathrin Skubch, Mihyun Kang, Oliver Cooley, Amin Coja-Oghlan

Publikováno v: Random Structures & Algorithms. 51:459-482

The k-core, defined as the maximal subgraph of minimum degree at least k, of the random graph G(n,p) has been studied extensively. In a landmark paper Pittel, Wormald and Spencer [J Combin Theory Ser B 67 (1996), 111–151] determined the threshold d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8afd9a7126c87994363526df93ecac06
https://doi.org/10.1002/rsa.20712