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

Juergen Herzog; Takayuki Hibi; Satoshi Murai; Ngo Viet Trung; Xinxian Zheng

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

Combinatorics 2008-12-01 v2

Authors: Juergen Herzog , Takayuki Hibi , Satoshi Murai , Ngo Viet Trung , Xinxian Zheng

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 $i > 1$ .

Keywords

kruskal-katona theorem clique complexes chordal graphs strongly chordal graphs shellability h-vector

Cite

@article{arxiv.math/0606477,
  title  = {Kruskal--Katona type theorems for clique complexes arising from chordal and strongly chordal graphs},
  author = {Juergen Herzog and Takayuki Hibi and Satoshi Murai and Ngo Viet Trung and Xinxian Zheng},
  journal= {arXiv preprint arXiv:math/0606477},
  year   = {2008}
}

Comments

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

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

Abstract

Keywords

Cite

Comments

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