Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Node-balancing by edge-increments   Suppose you are given a graph $G=(V,E)$ with a weight assignment
$w:V\rightarrow\mathbb{Z}$ and that your objective is to modify $w$ using legal
steps such that all vertices will have the same weight, where in each legal
step you are allowed to choose an edge and increment the weights of its end
points by $1$.
  In this paper we study several variants of this problem for graphs and
hypergraphs. On the combinatorial side we show connections with fundamental
results from matching theory such as Hall's Theorem and Tutte's Theorem. On the
algorithmic side we study the computational complexity of associated decision
problems.
  Our main results are a characterization of the graphs for which any initial
assignment can be balanced by edge-increments and a strongly polynomial-time
algorithm that computes a balancing sequence of increments if one exists.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph