Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Half-regular factorizations of the complete bipartite graph   We consider a bipartite version of the color degree matrix problem. A
bipartite graph $G(U,V,E)$ is half-regular if all vertices in $U$ have the same
degree. We give necessary and sufficient conditions for a bipartite degree
matrix (also known as demand matrix) to be the color degree matrix of an
edge-disjoint union of half-regular graphs. We also give necessary and
sufficient perturbations to transform realizations of a half-regular degree
matrix into each other. Based on these perturbations, a Markov chain Monte
Carlo method is designed in which the inverse of the acceptance ratios are
polynomial bounded.
  Realizations of a half-regular degree matrix are generalizations of Latin
squares, and they also appear in applied neuroscience.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess