On Graphs and the Gotsman-Linial Conjecture for d = 2
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.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2017
- DOI:
- 10.48550/arXiv.1709.06650
- arXiv:
- arXiv:1709.06650
- Bibcode:
- 2017arXiv170906650K
- Keywords:
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- Computer Science - Discrete Mathematics;
- Mathematics - Combinatorics
- E-Print:
- 15 pages