Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum degree thresholds for bipartite graph tiling   For any bipartite graph $H$, we determine a minimum degree threshold for a
balanced bipartite graph $G$ to contain a perfect $H$-tiling. We show that this
threshold is best possible up to a constant depending only on $H$.
Additionally, we prove a corresponding minimum degree threshold to guarantee
that $G$ has an $H$-tiling missing only a constant number of vertices. Our
threshold for the perfect tiling depends on either the chromatic number
$\chi(H)$ or the critical chromatic number $\chi_{cr}(H)$ while the threshold
for the almost perfect tiling only depends on $\chi_{cr}(H)$. Our results
answer two questions of Zhao. They can be viewed as bipartite analogs to the
results of Kuhn and Osthus and of Shokoufandeh and Zhao.

8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th