Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal graphs for hamiltonian extension   For every $n\ge 3$ we determine the minimum number of edges of graph with $n$
vertices such that for any non edge $xy$ there exits a hamiltonian cycle
containing $xy$.

30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph