Kruskal--Katona type theorems for clique complexes arising from chordal and strongly chordal graphs
Abstract
A forest is the clique complex of a strongly chordal graph and a quasi-forest is the clique complex of a chordal graph. Kruskal--Katona type theorems for forests, quasi-forests, pure forests and pure quasi-forests will be presented. In addition, it will be shown that a quasi-forest is shellable if and only if its h-vector (h0, h1, h2, ...) satisfies hi = 0 for i > 1.
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