Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Partition of graphs with maximum degree ratio   Given a graph $G$ and a non trivial partition $(V_1,V_2)$ of its vertex-set,
the satisfaction of a vertex $v\in V_i$ is the ratio between the size of it's
closed neighborhood in $V_i$ and the size of its closed neighborhood in $G$.
The worst ratio over all the vertices defines the quality of the partition. We
define $q(G)$ the degree ratio of a graph as the maximum of the worst ratio
over all the non trivial partitions. We give bounds and exact values of $q(G)$
for some classes of graphs. We also show some complexity results for the
associated optimization or decision problems.

20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc