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arXiv · 1009.3900

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

Jonathan Ariel Barmak
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Abstract

For each finite simple graph $G$, Aharoni, Berger and Ziv consider a recursively defined number $ψ(G) \in \mathbb{Z}\cup \{+ \infty \}$ 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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Jonathan Ariel Barmak. 2010-09-20. The word problem and the Aharoni-Berger-Ziv conjecture on the connectivity of independence complexes. https://arxiv.org/abs/1009.3900

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