Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Making spanning graphs   We prove that for each $D\ge 2$ there exists $c>0$ such that whenever $b\le
c\big(\tfrac{n}{\log n}\big)^{1/D}$, in the $(1:b)$ Maker-Breaker game played
on $E(K_n)$, Maker has a strategy to guarantee claiming a graph $G$ containing
copies of all graphs $H$ with $v(H)\le n$ and $\Delta(H)\le D$. We show further
that the graph $G$ guaranteed by this strategy also contains copies of any
graph $H$ with bounded maximum degree and degeneracy at most $\tfrac{D-1}{2}$.
This lower bound on the threshold bias is sharp up to the $\log$-factor when
$H$ consists of $\tfrac{n}{3}$ vertex-disjoint triangles or $\tfrac{n}{4}$
vertex-disjoint $K_4$-copies.

1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio