  If the twist numbers of a collection of oriented alternating link diagrams
are bounded, then the Alexander polynomials of the corresponding links have
bounded euclidean Mahler measure (see Definition 1.2). The converse assertion
does not hold. Similarly, if a collection of oriented link diagrams, not
necessarily alternating, have bounded twist numbers, then both the Jones
polynomials and a parametrization of the 2-variable Homflypt polynomials of the
corresponding links have bounded Mahler measure.
