Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 10-Gabriel graphs are Hamiltonian   Given a set $S$ of points in the plane, the $k$-Gabriel graph of $S$ is the
geometric graph with vertex set $S$, where $p_i,p_j\in S$ are connected by an
edge if and only if the closed disk having segment $\bar{p_ip_j}$ as diameter
contains at most $k$ points of $S \setminus \{p_i,p_j\}$. We consider the
following question: What is the minimum value of $k$ such that the $k$-Gabriel
graph of every point set $S$ contains a Hamiltonian cycle? For this value, we
give an upper bound of 10 and a lower bound of 2. The best previously known
values were 15 and 1, respectively.

37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph