Independence complexes of hypergraphs and bounded degree complexes

Takahiro Matsushita

Independence complexes of hypergraphs and bounded degree complexes

Combinatorics 2022-02-25 v2

Authors: Takahiro Matsushita

Abstract

The bounded degree complex $BD(G,\lambda)$ is a generalization of the matching complexes of a graph. In this paper, we show that the bounded degree complex of a forest is shellable, by using independence complexes of hypergraphs. We obtain a wedge decomposition result of bounded degree complexes when a graph $G$ has a leaf

Keywords

graph theory phylogenetic trees trees

Cite

@article{arxiv.2004.13281,
  title  = {Independence complexes of hypergraphs and bounded degree complexes},
  author = {Takahiro Matsushita},
  journal= {arXiv preprint arXiv:2004.13281},
  year   = {2022}
}

Comments

The proof of this paper had a flaw. In fact, every chordal clutter is chordal but it is not true that the independence complex of a chordal "hypergraph" is not shellable in general. Correcting the proof may not be difficult, but a stronger result is already known; see "Vertex decomposability of complexes associated to forests" by Anurag Singh. So I withdraw this paper

Independence complexes of hypergraphs and bounded degree complexes

Abstract

Keywords

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