Domestic fares with roundtrip booking and min stay requirements have become rarer over the years with the rise of LCCs like B6 and WN who don't have them (AS, although considered a legacy, also doesn't have them). But they have remained prevalent on DL out of hostage hubs like DTW and MSP with not much LCC competition (DL doesn't really even try to match ULCC fares). PHX having a large WN presense sees far fewer domestic DL fares with roundtrip booking/min stay requirements. PHX-ATL is an exception due to DL dominance on route and hub on ATL end. Domestic fare filings are symmetric.

On PHX-ATL, the cheapest roundtrip fares (XFVNH3MF) have Tue/Wed/Sat flight requirements (these are $418.20 roundtrip in Main). There's another roundtrip fare filing for slightly more (XFVNA5MF) that also allows Mon/Thu flights. There's yet another one (TFXNA0ME) that has no day of travel requirements. The AP requirements are pretty lengthy (21 days for the X fares and 45 days for the T fare). These are just the cheapest roundtrip fare filings (there are numerous other ones). The min stay requirements on these are fairly complex (it's not as simple as just a Saturday night stay and you can potentially book them for flights with a Satuday return without staying overnight on a Saturday). The min stay requirements found on delta.com (below) are only partial listings (the full section found on EF is actually much, much longer). The fifth position in fare basis code on domestic fares indicate day of travel requirements -- 3=Tue/Wed/Sat, 5= Mon/Tue/Wed/Thu/Sat, 0=no day of travel restrictions.



The cheapest one-way Main fares on PHX-ATL are UAWQA0ML fares for $319.10 one way. These have a 30 day AP. When the 2nd position in fare basis code is an A, there are no roundtrip booking requirements (you'll notice above that the fares with roundtip booking requirements all have an F in 2nd position). The 3rd position is used for the AP requirements on fare. X=45 days, W=30 days, V=21 days, U=14 days, 7=7 days, 3=3 days, 0=0 days.