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City Councilman Eric Garcetti and Controller Wendy Greuel are running neck-and-neck in Tuesday's Los Angeles mayoral primary, according to a new USC Sol Price School of Public Policy/Los Angeles Times poll released on Sunday, but a healthy share of likely voters remain undecided in the top-two primary or say they could change their minds.

Garcetti leads Greuel in the poll, conducted last Sunday through Wednesday, 27 percent to 25 percent. But two other candidates remain in striking distance: Republican attorney Kevin James, with 15 percent, and Councilwoman Jan Perry, at 14 percent. Former tech executive Emanuel Pleitez is well back, at 5 percent. Fourteen percent of likely voters are undecided.

But among those likely voters who say they are "definitely" voting for their preferred candidate, Garcetti and Greuel are in more tenuous positions. Among these voters, both frontrunners earn 12 percent of the vote, with James close behind, with 10 percent.

"It is notable how much this race is still in flux a week out," pollster Amy Levin told the Los Angeles Times. Levin's firm, the Democratic polling outfit Benenson Strategy Group, conducted the poll, along with the Republican M4 Strategies. The poll surveyed 500 likely voters, and results carry a margin of error of plus-or-minus 4.4 percentage points.

Assuming no candidate earns a majority of the vote in the primary, the top two finishers will advance to the nonpartisan general election on May 21.