And chordal graphs also have several other characterizations... See e.g. en.wikipedia.org/wiki/Chordal_graph

From the summary in mathreviews and Wegner's paper, it sounds like one could go either way. Indeed it follows easily from the simplicial vertex condition, but it also follows easily from first principles. ($\Delta$ is the clique complex of a graph, since otherwise it contains a simplex boundary as an induced subcomplex; this graph is chordal since otherwise it contains a 1-sphere as an induced subcomplex.)

The Fröberg reference is just the first one I know -- I wouldn't be at all surprised if there were an earlier one. (Please tell me if you find the paper you're thinking of.) The characterization is a pleasing theorem with a fairly easy proof, and indeed often rediscovered. <br> Fröberg's paper did seem to stir up quite a bit of activity in the commutative algebra and algebraic combinatorics literature.