Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isolation of $k$-cliques   For any positive integer $k$ and any $n$-vertex graph $G$, let $\iota(G,k)$
denote the size of a smallest set $D$ of vertices of $G$ such that the graph
obtained from $G$ by deleting the closed neighbourhood of $D$ contains no
$k$-clique. Thus, $\iota(G,1)$ is the domination number of $G$. We prove that
if $G$ is connected, then $\iota(G,k) \leq \frac{n}{k+1}$ unless $G$ is a
$k$-clique or $k = 2$ and $G$ is a $5$-cycle. The bound is sharp. The case
$k=1$ is a classical result of Ore, and the case $k=2$ is a recent result of
Caro and Hansberg. Our result solves a problem of Caro and Hansberg.

11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat