Graph Theory versus Minimum Rank for Index Coding
  We obtain novel index coding schemes and show that they provably outperform all previously known graph theoretic bounds proposed so far. Further, we establish a rather strong negative result: all known graph theoretic bounds are within a logarithmic factor from the chromatic number. This is in striking contrast to minrank since prior work has shown that it can outperform the chromatic number by a polynomial factor in some cases. The conclusion is that all known graph theoretic bounds are not much stronger than the chromatic number. 
Karthikeyan Shanmugam, Alexandros G. Dimakis and Michael Langberg
cs.IT math.IT