2 papers
math.CO2026
A direct inductive proof of the sharp Merino--Welsh threshold for matroids
Jungang Chen, Jiaxin Xie
Motivated by the Merino--Welsh conjecture, we consider the smallest , denoted by , for which the inequality holds for every loopless an…
math.CO2026
Quantitative Merino--Welsh inequalities for joins
Jungang Chen, Jiaxin Xie
For a connected graph \(G\), let \[ Q(G)=\frac{T(G;2,0)T(G;0,2)}{T(G;1,1)^2}. \] We obtain quantitative lower bounds for \(Q\) under the graph join operation. If \(A\) and \(B\) ar…