I am curious, what is it about eucalyptus trees that prompts the name of "Gum".
I know of 2 trees in the US natives that have gum in the name, sweet gum. Liquidamber styratafolio, which has  slightly sweet sap that occurs as a material similar to chewing gum and  black tupelo, aka black gum, Nyata sylvatica, which, to my limited knowledge, makes nothing similar to chewing gum.

Believe are known as gum trees because they exude copious kino ( gum ), from any break in the bark.

Thanks for the links, jaeger88. We have a few eucalypts here in the US that were imported from Australia, especially in California. (In fact, I don't know of them anywhere else in the US.) I used to salvage wood from them when the city of San Diego would cut them down or clear blow-downs. None of the species I ran across here in the States exuded 'gum'. On the contrary actually, I thought they were a bit 'drier' than other local trees. However, when I was in Australia I saw what variety there is among eucalyptus. There must be hundreds of species. I am sure that several, if not many, exude 'gum'.

Paul

I do know of some plantings of eucalyptus trees, specie not known, in S. Texas, mostly along H. 281.
All I have seen are south of San Antonio, so I would infer that they are at least somewhat frost tender.