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Projective Dimension, Graph Domination Parameters, and Independence Complex Homology (1110.2841v2)
Published 13 Oct 2011 in math.AC and math.CO
Abstract: 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.