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We highlight the author&#8217;s recent proof that real roots of all-terminal reliability polynomials of simple graphs are dense in <code>[-1,0]U{1}<\/code>; refining the same theorem proved for multigraphs by Brown and Colbourn (1992).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We discuss why studying roots of combinatorial polynomials plays an important role in understanding the underlying combinatorics of the structures these polynomials encode. We highlight the author&#8217;s recent proof that real roots of all-terminal reliability polynomials of simple graphs are dense in <code>[-1,0]U{1}<\/code>; refining the same theorem proved for multigraphs by Brown and Colbourn 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