A Proof of Delta Conjecture

Abstract

By finding orthogonal representation for a family of simple connected called $\delta$-graphs it is possible to show that $\delta$-graphs satisfy delta conjecture. An extension of the argument to graphs of the form $\overline{P_{\Delta (G)+2}\bigsqcup G}$ where $P_{\Delta (G)+2}$ is a path and $G$ is a simple connected graph it is possible to find an orthogonal representation of $\overline{P_{\Delta (G)+2}\bigsqcup G}$ in ${\mathbb{R}}^{\Delta (G)+1}$. As a consequence we prove delta conjecture.

12 pages, 4 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:1610.00792, arXiv:1806.05562