Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A conjecture on bipartite graphical regular representations   In this paper we are concerned with the classification of the finite groups
admitting a bipartite DRR and a bipartite GRR.
  First, we find a natural obstruction in a finite group for not admitting a
bipartite GRR. Then we give a complete classification of the finite groups
satisfying this natural obstruction and hence not admitting a bipartite GRR.
Based on these results and on some extensive computer computations, we state a
conjecture aiming to give a complete classification of the finite groups
admitting a bipartite GRR.
  Next, we prove the existence of bipartite DRRs for most of the finite groups
not admitting a bipartite GRR found in this paper. Actually, we prove a much
stronger result: we give an asymptotic enumeration of the bipartite DRRs over
these groups. Again, based on these results and on some extensive computer
computations, we state a conjecture aiming to give a complete classification of
the finite groups admitting a bipartite DRR.

17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
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
14
The categories of this paper are: math-ph