Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Minimum Number of Hamiltonian Cycles in Regular Graphs   A graph construction that produces a k-regular graph on n vertices for any
choice of k >= 3 and n = m(k+1) for integer m >= 2 is described. The number of
Hamiltonian cycles in such graphs can be explicitly determined as a function of
n and k, and empirical evidence is provided that suggests that this function
gives a tight upper bound on the minimum number of Hamiltonian cycles in
k-regular graphs on n vertices for k >= 5 and n >= k + 3. An additional graph
construction for 4-regular graphs is described for which the number of
Hamiltonian cycles is superior to the above function in the case when k = 4 and
n >= 11.

29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an