Mathematics Colloquia and Seminars

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To every (hyper)graph G with vertex set {1,...,n} one can associate its 'edge ideal' I_G, by definition the ideal in k[x_1,...,x_n] generated by monomials corresponding to the edges of G. The natural goal is to then relate the algebraic properties of I_G to the combinatorial properties of the underlying graph G. An important result in this vein is a well-known result of Froberg from 1990 which says that an edge ideal I_G has a 'linear' resolution if and only if the complement of G is a 'chordal' graph. We will define and discuss these notions (in particular those with the quotations around them) and, if time permits, sketch a proof of Froberg's result.