Projective Dimension, Graph Domination Parameters, and Independence   Complex Homology
  We construct several pairwise-incomparable bounds on the projective dimensions of edge ideals. Our bounds use combinatorial properties of the associated graphs; in particular we draw heavily from the topic of dominating sets. Through Hochster's Formula, these bounds recover and strengthen existing results on the homological connectivity of graph independence complexes. 
Hailong Dao, Jay Schweig
math.AC math.CO