  We establish a spectral gap for stable commutator length (scl) of integral
chains in right-angled Artin groups (RAAGs). We show that this gap is not
uniform, i.e. there are RAAGs and integral chains with scl arbitrarily close to
zero. We determine the size of this gap up to a multiplicative constant in
terms of the opposite path length of the defining graph. This result is in
stark contrast with the known uniform gap 1/2 for elements in RAAGs. We prove
an analogous result for right-angled Coxeter groups.
  In a second part of this paper we relate certain integral chains in RAAGs to
the fractional stability number of graphs. This has several consequences:
Firstly, we show that every rational number q>=1 arises as the stable
commutator length of an integral chain in some RAAG. Secondly, we show that
computing scl of elements and chains in RAAGs is NP hard. Finally, we
heuristically relate the distribution of scl for random elements in the free
group to the distribution of fractional stability number in random graphs.
  We prove all of our results in the general setting of graph products. In
particular all above results hold verbatim for right-angled Coxeter groups.
