alt Hacker NewsI'd argue there's only three "major" carriers: American, United, and Delta.
The rest, such as Frontier, JetBlue, Southwest, Allegiant - are all discount and/or regional airlines.
For example, allegiant flies to most cities secondary airports that are 1-2 hours drive from the city.
EDIT: It's really 4 equally large ones by passenger miles:
* 1 Delta Air Lines 17.8%
* 2 American Airlines 17.5%
* 3 Southwest Airlines 17.3%
* 4 United Airlines 16.0%
The rest are sub 10%
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Which is actually worse than the regulated airlines were before Jimmy Carter deregulated them. When prices were uniformly set by the government, there were 11 "trunk" airlines in 1978, 9 regional airlines, and three unregulated intrastate airlines- one was Southwest (flying just in Texas, the other two, Air California and PSA, were just in California). Those 23 airlines are now down basically to the Big 4 plus 3 little ones (Alaska, Jet Blue, Frontier). Airline tickets were more expensive- well, the prices were about the same number of dollars but thanks to inflation that's a lot less buying power.
Southwest and Alaska are absolutely major carriers. Not the absolute largest perhaps but major. Alaska is certainly not discount, and despite the name is not particularly regional.
To your edit, Alaska is something like 9.9%. Technically below 10%, but barely.