Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Largest 2-regular subgraphs in 3-regular graphs   For a graph $G$, let $f_2(G)$ denote the largest number of vertices in a
$2$-regular subgraph of $G$. We determine the minimum of $f_2(G)$ over
$3$-regular $n$-vertex simple graphs $G$. To do this, we prove that every
$3$-regular multigraph with exactly $c$ cut-edges has a $2$-regular subgraph
that omits at most $\max\{0,\lfloor (c-1)/2\rfloor\}$ vertices. More generally,
every $n$-vertex multigraph with maximum degree $3$ and $m$ edges has a
$2$-regular subgraph that omits at most $\max\{0,\lfloor
(3n-2m+c-1)/2\rfloor\}$ vertices. These bounds are sharp; we describe the
extremal multigraphs.

7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol