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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 o
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