Kruskal--Katona type theorems for clique complexes arising from chordal and strongly chordal graphs

Details Kruskal--Katona type theorems for clique complexes arising from chordal and strongly chordal graphs Kruskal--Katona type theorems for clique complexes arising from chordal and strongly chordal graphs

2006-06-20

arxiv.org/abs/math/0606477v2

Combinatorica 28 (2008), 315--323

Mathematics

Combinatorics

7pages, simplify the characterization of face vectors, remove appendix, add references

Scientific paper

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 $(h_0, h_1, h_2, ...)$ satisfies $h_i = 0$ for $i > 1$.

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