  We revisit the well-studied problem of triangle count estimation in graph
streams. Given a graph represented as a stream of $m$ edges, our aim is to
compute a $(1\pm\varepsilon)$-approximation to the triangle count $T$, using a
small space algorithm. For arbitrary order and a constant number of passes, the
space complexity is known to be essentially $\Theta(\min(m^{3/2}/T,
m/\sqrt{T}))$ (McGregor et al., PODS 2016, Bera et al., STACS 2017).
  We give a (constant pass, arbitrary order) streaming algorithm that can
circumvent this lower bound for \emph{low degeneracy graphs}. The degeneracy,
$\kappa$, is a nuanced measure of density, and the class of constant degeneracy
graphs is immensely rich (containing planar graphs, minor-closed families, and
preferential attachment graphs). We design a streaming algorithm with space
complexity $\widetilde{O}(m\kappa/T)$. For constant degeneracy graphs, this
bound is $\widetilde{O}(m/T)$, which is significantly smaller than both
$m^{3/2}/T$ and $m/\sqrt{T}$. We complement our algorithmic result with a
nearly matching lower bound of $\Omega(m\kappa/T)$.
