  Let $\chi(G$) and $\chi_f(G)$ denote the chromatic and fractional chromatic
numbers of a graph $G$, and let $(n^+ , n^0 , n^-)$ denote the inertia of $G$.
We prove that:
  \[ 1 + \max\left(\frac{n^+}{n^-} , \frac{n^-}{n^+}\right) \le \chi(G) \mbox{
and conjecture that } 1 + \max\left(\frac{n^+}{n^-} , \frac{n^-}{n^+}\right)
\le \chi_f(G) \]
  We investigate extremal graphs for these bounds and demonstrate that this
inertial bound is not a lower bound for the vector chromatic number. We
conclude with a discussion of asymmetry between $n^+$ and $n^-$, including some
Nordhaus-Gaddum bounds for inertia.

Combinatorics