Author

Jun-Gang Chen

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Preprint Sep 2026

Quantitative Merino--Welsh inequalities for joins

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 $B$ are arbitrary simple graphs of orders $3\le a\le b$, then $Q(A\vee B)$ admits an explicit lower bound depending only on $a$ and $b$, a...

Jun-Gang Chen, Jia-Xin Xie · 1 citation · ⚡1

Preprint Oct 2026

A direct inductive proof of the sharp Merino--Welsh threshold for matroids

Motivated by the Merino--Welsh conjecture, we consider the smallest $c\ge0$, denoted by $c_*$, for which the inequality $T_M(c,0)T_M(0,c)\ge T_M(1,1)^2$ holds for every loopless and coloopless finite matroid $M$. The counterexamples constructed by Beke, Cs\'aji, Csikv\'ari, and Pituk [\emph{Adv. Math.} \textbf{446} (20...

Jun-Gang Chen, Jia-Xin Xie · 0 citations