Mayor Adrian Fenty’s hometown ward isn’t giving its full support.

According to a poll commissioned by Councilman Jim Graham’s campaign, Fenty is leading D.C. Council Chairman Vince Gray 43 percent to 37 percent in Ward 1. That’s a tight race for the mayor who grew up in the ward and whose parents still own a popular business in the area.

But with nearly 18 percent of the 300 Democratic voters polled saying they’re undecided, there’s still plenty of room for Fenty or Gray to make a strong move.

Graham, by the way, is dominating his race. The poll says he’s sitting on a comfortable 68 percent of the vote. Graham’s two competitors, Jeff Smith and Bryan Weaver, split 15 percent of the vote and 17 percent are undecided.