irrimn: This would work perfectly if people routinely sold pets that had been researched. But they don't, most pets in auctions haven't been researched and so won't show up on any filters for genes, only for species and gender (and stats I think)
There is no way to search for generically 'green' genes on unresearched pets.
Ok, except if no genes are researched then how can the person who bred it know what the genes are anyways? The only case in point would be where the genes give green stats but if that's the only purpose I would rather see a search option for GREEN STATS. Then you could filter all pets by, for example, "All pets with green bite damage". Then that'd of course include sharp teeth, double incisors, saber-toothed, acid spitting, fire breathing, lightning calling, solid beak, massive beak, solid horn, and diamond horn. If the genes aren't researched then there would be no way to know which without doing the math (which takes all of 2 seconds) but at least then you'd know they had a dominant gene that affects bite -- without needing to be researched.
Plus I think ADs placed on the auction listing would just be annoying and clutter up the page.