Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On fractionality of the path packing problem   In this paper, we study fractional multiflows in undirected graphs. A
fractional multiflow in a graph G with a node subset T, called terminals, is a
collection of weighted paths with ends in T such that the total weights of
paths traversing each edge does not exceed 1. Well-known fractional path
packing problem consists of maximizing the total weight of paths with ends in a
subset S of TxT over all fractional multiflows. Together, G,T and S form a
network. A network is an Eulerian network if all nodes in N\T have even
degrees.
  A term "fractionality" was defined for the fractional path packing problem by
A. Karzanov as the smallest natural number D so that there exists a solution to
the problem that becomes integer-valued when multiplied by D. A. Karzanov has
defined the class of Eulerian networks in terms of T and S, outside which D is
infinite and proved that whithin this class D can be 1,2 or 4. He conjectured
that D should be 1 or 2 for this class of networks. In this paper we prove this
conjecture.

23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin