Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optimal stopping for many connected components in a graph   We study a new optimal stopping problem: Let $G$ be a fixed graph with $n$
vertices which become active on-line in time, one by another, in a random
order. The active part of $G$ is the subgraph induced by the active vertices.
Find a stopping algorithm that maximizes the expected number of connected
components of the active part of $G$. We prove that if $G$ is a $k$-tree, then
there is no asymptotically better algorithm than `wait until $\frac{1}{k+1}$
fraction of vertices'. The maximum expected number of connected components
equals to $$\left(\frac{k^k}{(k+1)^{k+1}}+o(1)\right)n.$$

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The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph