Help with damaged Tif-Green grass

I have a large yard with Tif green (summer type Bermuda). The lawn were damaged by weeds. Most the area under the tree are now bare soil.
I would like to overseed with some type of summer bermuda grass. What's type? I lived in the SW Desert. Thanks
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DaViT wrote:

How could bermuda be damaged by weeds? Anyway, it sounds like your problems is shade. Bermuda will not grow under trees, period. It will not stand any shade at all.
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Peanut is right, shade is a big no-no for Bermuda. If you want to stay with a warm-season grass you might try St. Augustine. It can't go much further north than zone 8 or southern zone 7, freezes out north of there. Your other option might be to prune the tree up so that sunlight can reach underneath. Tif varieties need at least 6 or 7 hours of sun a day.

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