Abstract
A 2 -nearly Platonic graph of type ( k | d ) is a k -regular planar graph with f faces, f − 2 of which are of size d and the remaining two are of sizes d 1 , d 2 , both different from d . Such a graph is called balanced if d 1 = d 2 . We show that all connected 2 -nearly Platonic graphs are necessarily balanced. This proves a recent conjecture by Keith, Froncek, and Kreher.
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