  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.
