The word problem and the Aharoni-Berger-Ziv conjecture on the connectivity of independence complexes

Details The word problem and the Aharoni-Berger-Ziv conjecture on the connectivity of independence complexes The word problem and the Aharoni-Berger-Ziv conjecture on the connectivity of independence complexes

2010-09-20

arxiv.org/abs/1009.3900v1

Mathematics

Combinatorics

2 pages

Scientific paper

For each finite simple graph $G$, Aharoni, Berger and Ziv consider a
recursively defined number $\psi (G) \in \mathbb{Z}\cup \{+ \infty \}$ which
gives a lower bound for the topological connectivity of the independence
complex $I_G$. They conjecture that this bound is optimal for every graph. We
use a result of recursion theory to give a short disproof of this claim.

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