Let G be a simple (i.e., no loops and no multiple edges) graph. We investigate the question of how to modify G combinatorially to obtain a sequentially Cohen-Macaulay graph. We focus on modifications given by adding configurations of whiskers to G, where to add a whisker one adds a new vertex and an edge connecting this vertex to an existing vertex in G. We… (More)
and associated primes of powers of monomial ideals. Associated primes of monomial ideals and odd holes in graphs. A conjecture on critical graphs and connections to the persistence of associated primes.