Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cones of closed alternating walks and trails   Consider a graph whose edges have been colored red and blue. Assign a
nonnegative real weight to every edge so that at every vertex, the sum of the
weights of the incident red edges equals the sum of the weights of the incident
blue edges. The set of all such assignments forms a convex polyhedral cone in
the edge space, called the \emph{alternating cone}. The integral (respectively,
  $\{0,1\}$) vectors in the alternating cone are sums of characteristic vectors
of closed alternating walks (respectively, trails). We study the basic
properties of the alternating cone, determine its dimension and extreme rays,
and relate its dimension to the majorization order on degree sequences. We
consider whether the alternating cone has integral vectors in a given box, and
use residual graph techniques to reduce this problem to searching for a closed
alternating trail through a given edge. The latter problem, called alternating
reachability, is solved in a companion paper along with related results.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an