Zobrazeno 1 - 7
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pro vyhledávání: '"Kontogeorgiou, George"'
Autor:
Kontogeorgiou, George, Stein, Maya
We show that for each natural number $n$ the clique $K_n$ has a weakly separating path system of size $n+2$, improving the previous best known upper bound of $(1+o(1))n$. Since $n-1$ is a lower bound, this is almost tight.
Comment: 7 pages
Comment: 7 pages
Externí odkaz:
http://arxiv.org/abs/2403.08210
A recent development in graph theory is to study local separators, vertex sets that need not separate graphs globally but just locally. We use this idea to conjecture an extension of Stallings' theorem to finite nilpotent groups. We provide an exampl
Externí odkaz:
http://arxiv.org/abs/2403.07776
Autor:
Kontogeorgiou, George
We produce a new, shorter construction of a minor-universal planar graph.
Comment: 5 pages, 3 figures
Comment: 5 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/2309.06669
Autor:
Kontogeorgiou, George, Winter, Martin
For every sufficiently well-behaved function $g:\mathbb{R}_{\ge 0}\rightarrow\mathbb{R}_{\ge 0}$ that grows at least linearly and at most exponentially we construct a tree $T$ of uniform volume growth $g$, that is, $$C_1\cdot g(r/4)\le |B_{T}(v,r)| \
Externí odkaz:
http://arxiv.org/abs/2212.01883
We prove that a group $\Gamma$ admits a discrete topological (equivalently, smooth) action on some simply-connected 3-manifold if and only if $\Gamma$ has a Cayley complex embeddable -- with certain natural restrictions -- in one of the following fou
Externí odkaz:
http://arxiv.org/abs/2208.09918
We want to efficiently find a specific object in a large unstructured set, which we model by a random $n$-permutation, and we have to do it by revealing just a single element. Clearly, without any help this task is hopeless and the best one can do is
Externí odkaz:
http://arxiv.org/abs/2008.11448
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