Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Triangle-tilings in graphs without large independent sets   We study the minimum degree necessary to guarantee the existence of perfect
and almost-perfect triangle-tilings in an $n$-vertex graph $G$ with sublinear
independence number. In this setting, we show that if $\delta(G) \ge n/3 +
o(n)$ then $G$ has a triangle-tiling covering all but at most four vertices.
Also, for every $r \ge 5$, we asymptotically determine the minimum degree
threshold for a perfect triangle-tiling under the additional assumptions that
$G$ is $K_r$-free and $n$ is divisible by $3$.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int