On the imaginary parts of chromatic roots
Jason I. Brown, David G. Wagner · Journal of Graph Theory · 2019
Abstract While much attention has been directed to the maximum modulus and maximum real part of chromatic roots of graphs of order (ie, with vertices), relatively little is known about the maximum imaginary part of such graphs. We prove that the maximum imaginary part can grow linearly in the order of the graph. We also show that for any fixed , almost every random graph in the Erdös‐Rényi model has a nonreal root.