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pro vyhledávání: '"Sorkin, Gregory"'
We study the 2-offer semirandom 3-uniform hypergraph model on $n$ vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect
Externí odkaz:
http://arxiv.org/abs/2401.00559
The semi-random graph process is an adaptive random graph process in which an online algorithm is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the algorithm independently and uniformly at random. The
Externí odkaz:
http://arxiv.org/abs/2311.05533
Autor:
Frieze, Alan, Sorkin, Gregory B.
We show that with high probability we can build a Hamilton cycle after at most $1.85 n$ rounds in a particular semi-random model. In this model, in one round, we are given a {uniform random} $v\in[n]$ and then we can add an {arbitrary} edge $\{v,w\}$
Externí odkaz:
http://arxiv.org/abs/2208.00255
Autor:
Sorkin, Gregory B.
This recreational mathematics article shows that the game of Snakes and Ladders is intransitive: square 69 has a winning edge over 79, which in turn beats 73, which beats 69. Analysis of the game is a nice illustration of Markov chains, simulations o
Externí odkaz:
http://arxiv.org/abs/2201.07004
The Ising antiferromagnet is an important statistical physics model with close connections to the {\sc Max Cut} problem. Combining spatial mixing arguments with the method of moments and the interpolation method, we pinpoint the replica symmetry brea
Externí odkaz:
http://arxiv.org/abs/2009.10483
Consider a complete graph $K_n$ with edge weights drawn independently from a uniform distribution $U(0,1)$. The weight of the shortest (minimum-weight) path $P_1$ between two given vertices is known to be $\ln n / n$, asymptotically. Define a second-
Externí odkaz:
http://arxiv.org/abs/1911.01151
Publikováno v:
Electron. J. Combin. 28 (2021), no. 1, Paper No. 1.20,-18
Recall that Janson showed that if the edges of the complete graph $K_n$ are assigned exponentially distributed independent random weights, then the expected length of a shortest path between a fixed pair of vertices is asymptotically equal to $(\log
Externí odkaz:
http://arxiv.org/abs/1910.08977
Autor:
Janson, Svante, Sorkin, Gregory B.
In a complete graph $K_n$ with edge weights drawn independently from a uniform distribution $U(0,1)$ (or alternatively an exponential distribution $\operatorname{Exp}(1)$), let $T_1$ be the MST (the spanning tree of minimum weight) and let $T_k$ be t
Externí odkaz:
http://arxiv.org/abs/1906.01533
Autor:
Sorkin, Gregory B.1 (AUTHOR) g.b.sorkin@lse.ac.uk
Publikováno v:
Mathematical Intelligencer. Dec2023, Vol. 45 Issue 4, p312-318. 7p.
We determine, asymptotically in $n$, the distribution and mean of the weight of a minimum-weight $k$-clique (or any strictly balanced graph $H$) in a complete graph $K_n$ whose edge weights are independent random values drawn from the uniform distrib
Externí odkaz:
http://arxiv.org/abs/1606.04925