Ralf Fröberg: On squarefree monomial rings with 2-linear resolution

Abstract: For a graph G with vertices \(V=\{v_1,\ldots,v_n\}\) and edges E, the edge ring k[G] is \(k[v_1,\ldots,v_n]/I\), where I is generated by all \(v_iv_j\) for which \((i,j)\in E\). For which graphs does k[G] have a linear resolution? Which Stanley-Reisner rings have 2-linear resolution? That a ring \(k[x_1,\ldots,x_n]/I=S/I\) has 2-linear resolution means that I is generated in degree 2 and has a linear resolution, equivalently that \(Tor_i^S(I,k)_j=0\) if \(j\ne i+2\). What are the Betti numbers of the skeletons of those complexes?