Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalization of the problem of Mariusz Meszka   Mariusz Meszka has conjectured that given a prime p=2n+1 and a list L
containing n positive integers not exceeding n there exists a near 1-factor in
K_p whose list of edge-lengths is L. In this paper we propose a generalization
of this problem to the case in which p is an odd integer not necessarily prime.
In particular, we give a necessary condition for the existence of such a near
1-factor for any odd integer p. We show that this condition is also sufficient
for any list L whose underlying set S has size 1, 2, or n. Then we prove that
the conjecture is true if S={1,2,t} for any positive integer t not coprime with
the order p of the complete graph. Also, we give partial results when t and p
are coprime. Finally, we present a complete solution for t<12.

19
The categories of this paper are: eess
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph