  Dimensional reduction occurs when the critical behavior of one system can be
related to that of another system in a lower dimension. We show that this
occurs for directed branched polymers (DBP) by giving an exact relationship
between DBP models in D+1 dimensions and repulsive gases at negative activity
in D dimensions. This implies relations between exponents of the two models:
$\gamma(D+1)=\alpha(D)$ (the exponent describing the singularity of the
pressure), and $\nu_{\perp}(D+1)=\nu(D)$ (the correlation length exponent of
the repulsive gas). It also leads to the relation $\theta(D+1)=1+\sigma(D)$,
where $\sigma(D)$ is the Yang-Lee edge exponent. We derive exact expressions
for the number of DBP of size N in two dimensions.
