This article accompanies the fable
The painting is from an interesting series of frescoes by Piero della Francesca called The Legend of the True Cross, painted in a church in Arezzo in the 1450's. In the legend, wood from the Garden of Eden survives through the centuries to become the cross on which Jesus will be crucified. In other panels the Jews (including Solomon) do their best to avoid blame for this by trying to hide or destroy the wood, which keyed into the particularly nasty anti-Semitic preaching of the time.
The image detail below, from the same frescoes, is interesting for similar reasons. This African figure is on a banner at a battle between the Byzantine Emperor Heraclius (the good guys) who are defeating the Persian Emperor Khosrow (the bad guys) for control of the sacred wood. Piero della Francesca has Jews and Moors (like this one) fighting for Khosrow, which is why the banner is torn as they go down to defeat.
As for the legend of the True Cross itself, it got its start, apparently, when St. Helena, the mother of Emperor Constantine, found it in Jerusalem some time before her death around 330 CE. She was quite prolific in finding sacred relics and building churches but this may have been her crowning achievement.
Nowadays the True Cross seems to exist in dozens of pieces, in Greece, Spain, Italy, France, Belgium, Ethiopia and so on.