Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spanning structures and universality in sparse hypergraphs   In this paper the problem of finding various spanning structures in random
hypergraphs is studied. We notice that a general result of Riordan [Spanning
subgraphs of random graphs, Combinatorics, Probability & Computing 9 (2000),
no. 2, 125-148] can be adapted from random graphs to random $r$-uniform
hypergaphs and provide sufficient conditions when a random $r$-uniform
hypergraph $\mathcal{H}^{(r)}(n,p)$ contains a given spanning structure a.a.s.
We also discuss several spanning structures such as cube-hypergraphs, lattices,
spheres and Hamilton cycles in hypergraphs.
  Moreover, we study universality, i.e. when does an $r$-uniform hypergraph
contain any hypergraph on $n$ vertices and with maximum vertex degree bounded
by $\Delta$? For $\mathcal{H}^{(r)}(n,p)$ it is shown that this holds for $p=
\omega \left((\ln n/n)^{1/\Delta}\right)$ a.a.s. by combining approaches taken
by Dellamonica, Kohayakawa, R\"odl and Ruci\'nski [An improved upper bound on
the density of universal random graphs, Random Structures Algorithms 46 (2015),
no. 2, 274-299] and of Ferber, Nenadov and Peter [Universality of random graphs
and rainbow embedding, Random Structures Algorithms, to appear]. Furthermore it
is shown that the random graph $G(n,p)$ for appropriate $p$ and explicit
constructions of universal graphs due to Alon, Capalbo, Kohayakawa, R\"odl,
Ruci\'nski and Szemer\'edi and Alon and Capalbo yield constructions of
universal hypergraphs that are sparser than the random hypergraph
$\mathcal{H}^{(r)}(n,p)$ with $p= \omega \left((\ln n/n)^{1/\Delta}\right)$.

23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg