On Graphs and the Gotsman-Linial Conjecture for d = 2
Discrete Mathematics
2017-09-21 v1 Combinatorics
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.
Cite
@article{arxiv.1709.06650,
title = {On Graphs and the Gotsman-Linial Conjecture for d = 2},
author = {Hyo Won Kim and Chris Maldonado and Jake Wellens},
journal= {arXiv preprint arXiv:1709.06650},
year = {2017}
}
Comments
15 pages