SAN FRANCISCO (AP) - Facebook's mystery "press event" on Tuesday could reveal a more robust search feature that would intensify the competition between the social networking giant and its rival Google Inc. Facebook is holding the event at 10 a.m. EST) at its Menlo Park, Calif., headquarters. The company has not said what it plans to announce. Last week, it invited bloggers and journalists to "come see what we're building." The company probably won't be showing off a new office building - unless it decided to make its invitation very literal. It's also unlikely to be unveiling a much-rumored "Facebook phone" - unless CEO Mark Zuckerberg has changed his mind recently. Last fall, as he'd done on numerous occasions, he publicly shot down speculation that Facebook was building its own smartphone. "It is so clearly the wrong strategy for us," Zuckerberg said at a September technology conference in his first public interview after Facebook's May initial public offering. It doesn't move the needle for us. As far as search goes, users would likely welcome a better way to sift through Facebook for people, businesses, events and everything else available on the vast online network. The company, whose much-ballyhooed initial public offering turned out to be a disappointment, may also talk about new advertising features. Facebook has been especially focused on building up is mobile advertising business, since most of its users access Facebook through smartphones and tablets. Research firm eMarketer estimates that Facebook, the No. 2 company in the U.S. mobile advertising market, had an 8.8 percent share last year - up from zero in 2011. That compared with No. 1 Google's 56.6 percent. This year, Facebook is expected to grow its share to 12.2 percent, while remaining far behind Google. Facebook, which has been calling itself a "mobile-first" company, has been growing thanks to increased use of its mobile apps, improving ad quality and its emerging advertising network, called Facebook Exchange, said Baird analyst Colin Sebastian in a recent note to investors. "Our field checks suggest that the recently launched Facebook Exchange is helping advertisers target consumers more effectively," he said. Sebastian thinks that over time, Facebook will make more money from mobile ads, helped by its increasing experience in the space, as well as its "ever-increasing user profile data."