Southwest Airlines (NYSE:LUV) has no love for its competitors.

Even as sky-high gas prices put a crimp in airline profits, Southwest seems determined to keep the pressure on its rivals. On Tuesday, the discount outfit announced a systemwide summer airfare sale with Web-only tickets available for as little as $39 one way.

Demand for air travel has picked up markedly in the past several months, and many airlines have reported steadily improving load factors. At the same time, fuel costs have soared, and major carriers, saddled with bloated cost structures, are still struggling to survive. Delta Air Lines (NYSE:DAL) is in do-or-die labor negotiations with its pilots, US Airways (NASDAQ:UAIR) may be on the edge of bankruptcy, and UAL's United Airlines has failed to receive loans from the government that it needs to emerge from bankruptcy. With demand high and fuel prices crushing results, these firms would love to hike fares.

Southwest, though, smells blood and seems determined to wage a price war. AMR's (NYSE:AMR) American Airlines, Northwest Airlines (NASDAQ:NWAC), and US Airways quickly matched the discounts in markets where they compete with Southwest. Low-price airline ATA Holdings (NASDAQ:ATAH) also instituted a series of sales yesterday.

And so Southwest and other low-cost leaders continue to reshape the industry. Tellingly, ATA is reportedly planning to start flying to Europe next year, threatening the traditional carriers' dominance of this stronghold. As competition remains hot on the domestic front, the implication for traditional carriers seems to be that there is no place to hide.

Fool contributor Brian Gorman is a freelance writer living in Chicago, Ill. He does not own shares of any companies mentioned here.