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

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

References in corpus (1)

• Face vectors of flag complexes

Cited by in corpus (1)

• A Kruskal-Katona Type Theorem for Graphs