Inconsequential results on the Merino-Welsh conjecture for Tutte polynomials

Joseph P. S. Kung

doi:10.1016/j.aam.2025.102866

paper

Inconsequential results on the Merino-Welsh conjecture for Tutte polynomials

arXiv:2105.01825 · doi:10.1016/j.aam.2025.102866

Abstract

The Merino-Welsh conjectures say that subject to conditions, there is an inequality among the Tutte-polynomial evaluations $T (M; 2, 0)$ , $T (M; 0, 2)$ , and $T (M; 1, 1)$ . We present three results on a Merino-Welsh conjecture. These results are "inconsequential" in the sense that although they imply a version of the conjecture for many matroids, they seem to be dead ends.