The fractional chromatic number of triangle-free subcubic graphs
  Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14/5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11 (which is roughly 2.909). 
David Ferguson, Tom\'a\v{s} Kaiser and Daniel Kr\'al'
math.CO