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On the imaginary parts of chromatic root
While much attention has been directed to the maximum modulus and maximum
real part of chromatic roots of graphs of order (that is, 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 Erd\"os-R\'enyi model has a non-real root.Comment: 4 figure
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