Algebraic Properties of Edge Ideals via Combinatorial Topology

  title={Algebraic Properties of Edge Ideals via Combinatorial Topology},
  author={Anton Dochtermann and Alexander Engstr{\"o}m},
  journal={Electr. J. Comb.},
We apply some basic notions from combinatorial topology to establish various algebraic properties of edge ideals of graphs and more general Stanley-Reisner rings. In this way we provide new short proofs of some theorems from the literature regarding linearity, Betti numbers, and (sequentially) Cohen-Macaulay properties of edge ideals associated to chordal, complements of chordal, and Ferrers graphs, as well as trees and forests. Our approach unifies (and in many cases strengthens) these results… CONTINUE READING
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