Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Upper bounds for the necklace folding problems   A necklace can be considered as a cyclic list of $n$ red and $n$ blue beads
in an arbitrary order, and the goal is to fold it into two and find a large
cross-free matching of pairs of beads of different colors. We give a
counterexample for a conjecture about the necklace folding problem, also known
as the separated matching problem. The conjecture (given independently by three
sets of authors) states that $\mu=\frac{2}{3}$, where $\mu$ is the ratio of the
`covered' beads to the total number of beads.
  We refute this conjecture by giving a construction which proves that $\mu \le
2 \nolinebreak - \nolinebreak \sqrt 2 < 0.5858$. Our construction also applies
to the homogeneous model: when we are matching beads of the same color.
Moreover, we also consider the problem where the two color classes not
necessarily have the same size.

19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex