Non-Bipartite Graphs of Small Mahler Measure

James McKee, Jonathan Cooley, Chris Smyth

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Abstract

The problem of describing the set of all small Mahler measures of polynomials with integer coefficients is a difficult one. One approach is to look for possible candidates among polynomials attached to combinatorial objects. In this paper we study the Mahler measure of polynomials coming from non-bipartite graphs: we classify all such graphs that have Mahler measure below the golden ration. This bound is natural in that it is found to be the smallest limit point of the set of Mahler measures of connected non-bipartite graphs.
Original languageEnglish
Pages (from-to)53-64
Number of pages12
JournalJournal of Combinatorics and Number Theory
Volume5
Issue number2
Publication statusPublished - 2014

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