Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Saturated Graphs of Prescribed Minimum Degree   A graph $G$ is $H$-saturated if it contains no copy of $H$ as a subgraph but
the addition of any new edge to $G$ creates a copy of $H$. In this paper we are
interested in the function sat$_{t}(n,p)$, defined to be the minimum number of
edges that a $K_{p}$-saturated graph on $n$ vertices can have if it has minimum
degree at least $t$. We prove that sat$_{t}(n,p) = tn - O(1)$, where the limit
is taken as $n$ tends to infinity. This confirms a conjecture of Bollob\'as
when $p = 3$. We also present constructions for graphs that give new upper
bounds for sat$_{t}(n,p)$ and discuss an analogous problem for saturated
hypergraphs.

16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int