The maximum Pfaffian number over graphs of genus at most g is at least (8/3)^g, improving prior linear lower bounds to exponential for bipartite and complete graphs.
Aufgabe 424.Archiv der Mathematik und Physik, 20:271, 1913
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Exponential Lower Bounds for the Pfaffian Number of Graphs
The maximum Pfaffian number over graphs of genus at most g is at least (8/3)^g, improving prior linear lower bounds to exponential for bipartite and complete graphs.