Zero-free regions for multivariate Tutte polynomials (alias Potts-model partition functions) of graphs and matroids

Understand

The chromatic polynomial P_G(q) of a loopless graph G is known to be nonzero (with explicitly known sign) on the intervals (-\infty,0), (0,1) and (1,32/27].

• Analogous theorems hold for the flow polynomial of bridgeless graphs and for the characteristic polynomial of loopless matroids.
• Here we exhibit all these results as special cases of more general theorems on real zero-free regions of the multivariate Tutte polynomial Z_G(q,v).
• The proofs are quite simple, and employ deletion-contraction together with parallel and series reduction.