On the smallest eigenvalues of $3$-colorable graphs

Zilin Jiang, Zhiyu Wang

We prove that the set of the smallest eigenvalues attained by $3$-colorable graphs is dense in $(-\infty ,-{\lambda }^{\ast })$, where ${\lambda }^{\ast }={\rho }^{1/2}+{\rho }^{-1/2}\approx 2.01980$ and $\rho$ is the po…