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arXiv · 1709.06650

On Graphs and the Gotsman-Linial Conjecture for d = 2

Hyo Won Kim·Chris Maldonado·Jake Wellens
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Abstract

We give an infinite class of counterexamples to the Gotsman-Linial conjecture when d = 2. On the other hand, we establish an asymptotic form of the conjecture for quadratic threshold functions whose non-zero quadratic terms define a graph with either low fractional chromatic number or few edges. Our techniques are elementary and our exposition is self-contained, if you're into that.

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Hyo Won Kim, Chris Maldonado, Jake Wellens. 2017-09-19. On Graphs and the Gotsman-Linial Conjecture for d = 2. https://arxiv.org/abs/1709.06650

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