Projective Dimension, Graph Domination Parameters, and Independence Complex Homology

2011/10/13 by Hailong Dao, Dao, Hailong, Jay Schweig +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.CO

paper · pdf · doi:10.48550/arxiv.1110.2841

Add references for Chapter 5 and 6. Add remarks 5.7 and 5.8

arxiv created 2011/10/22 · arxiv updated 2011/10/25

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.

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