Computing Semidefinite Programming Lower Bounds for the (Fractional) Chromatic Number Via Block-Diagonalization

@article{Gvozdenovic2008ComputingSP,
  title={Computing Semidefinite Programming Lower Bounds for the (Fractional) Chromatic Number Via Block-Diagonalization},
  author={Nebojsa Gvozdenovic and Monique Laurent},
  journal={SIAM Journal on Optimization},
  year={2008},
  volume={19},
  pages={592-615}
}
Recently we investigated in [SIAM J. Optim., 19 (2008), pp. 572–591] hierarchies of semidefinite approximations for the chromatic number χ(G) of a graph G. In particular, we introduced two hierarchies of lower bounds: the “ψ”-hierarchy converging to the fractional chromatic number and the “Ψ”-hierarchy converging to the chromatic number of a graph. In both hierarchies the first order bounds are related to the Lovász theta number, while the second order bounds would already be too costly to… CONTINUE READING