English

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.

Keywords

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

R2 v1 2026-06-22T21:48:49.212Z