John Connolly jaywalked across Warren Street, hustling to avoid an old red Geo hatchback. The vehicle showed little intention of hitting the brakes, even for a mayoral finalist and his entourage. And Connolly couldn’t afford to get run over just yet. He was rolling out his small business platform in Grove Hall, along the Dorchester-Roxbury line. He had businesses to tour and hands to shake. He had hours of walking ahead of him. In this neighborhood in particular, Connolly had plenty of legwork to do.

Connolly placed second in September’s Boston mayoral preliminary election, but he corralled just 8 percent of the vote in the precincts surrounding Grove Hall. The man he trailed in the preliminary, Marty Walsh, fared even worse in this neighborhood. Now, both mayoral finalists are scrambling to consolidate support in communities of color like Grove Hall — communities that largely passed over them in September.

Between the two of them, Walsh and Connolly combined to take 36 percent of the vote in September’s 12-way preliminary. That leaves most of the voters who turned out in the preliminary contest, plus some quantity of new voters in November’s final, up for grabs.

As Walsh and Connolly look to claim these votes, some neighborhoods look off-limits to one candidate or the other. Each finalist fared badly on the other’s geographic home turf. Walsh routinely lost West Roxbury precincts to Connolly by 20-plus points, while Walsh ran up margins as wide as 60 points in some parts of Dorchester. Connolly trounced Walsh in the Back Bay, Beacon Hill, and the South End, and he’s likely to deepen his support in those neighborhoods as he consolidates former Mike Ross supporters into his camp. Connolly also appears to be tightening his grip over East Boston. On the other hand, Hyde Park, which strongly backed City Councilor Rob Consalvo in September, looks wide open. (Click here for an interactive map comparing Walsh and Connolly’s vote totals across Boston.)

The biggest potential prizes, though, lie in Boston’s geographic center, where many of the city’s black and Hispanic residents reside. Majority-minority precincts cast 39 percent of the ballots in September’s preliminary contest. Neither Walsh nor Connolly ran particularly well in these precincts. (Click here for an interactive map detailing precincts where Walsh trailed in September’s preliminary election, and here for Connolly’s map.)

Connolly won just 8 of the city’s 112 majority-minority precincts. Walsh won 11. Each collected votes at roughly half the rate of Charlotte Golar Richie, who topped the ticket in Boston’s minority precincts. And when the two current mayoral finalists lost a majority-minority precinct, they tended to lose quite badly: Although each had some bright spots in majority-minority precincts, the median losing margin for both men hovered around 25 percent. Boston has 254 total precincts.

Richie’s vote haul in the city’s majority-minority precincts equaled Walsh and Connolly’s combined totals. Neither Walsh nor Connolly won a single majority-black precinct.

The upside to each candidate’s struggles in these neighborhoods is that neither heads into the race’s final weeks at a distinct disadvantage. There are 93 majority-minority precincts that both Connolly and Walsh lost; in two-thirds of these precincts, the mayoral finalists finished within 5 points of one another. A recent Suffolk University poll had Connolly up on Walsh by 7 points overall, but with one-third of black voters undecided about the two candidates. So tens of thousands of votes are up for grabs in Boston’s center, and Connolly and Walsh have equal amounts of work to do.

Walsh and Connolly have been staging campaign appearances in locations that underscore their need to grow in the city’s center.

Walsh trumpeted endorsements from former rivals John Barros and Felix Arroyo in Egleston Square — a corner of Jamaica Plain where Arroyo and Richie far outpaced the rest of the field. Standing in a neighborhood where he bested Walsh by 25 points, Arroyo told his supporters that Walsh’s campaign is “an extension of the work I’ve been doing,” that Walsh “believes that everybody in our city deserves opportunities to succeed.” Days later, Arroyo and Barros stood outside a Dorchester church, looking on as Richie, who led the mayoral field in majority-minority precincts, threw in with the Walsh campaign. “Let’s not let appearances, or the way he says ‘Chaaahlotte,’ fool you,” she said. “Marty is the new Boston, hands-down.”

Walsh talks about endorsements in terms of credibility and campaign infrastructure. He’s finding that, in neighborhoods that didn’t provide a rich haul of votes in September, the mention of the support he’s lined up from his former mayoral rivals has opened up conversations with voters who wouldn’t have been inclined to hear his pitch before. The endorsements don’t automatically deliver votes, but they at least get him in the door, which is more than Walsh had before. He’s also been enlisting volunteers who had been committed to other campaigns. “It’s important to get that infrastructure and support,” he says.

Walsh is also banking heavily on his Dorchester roots to open doors in places like Roxbury and Mattapan. He represents a racially diverse House district, and recognizes that a conversation about education on Bowdoin Avenue is going to unfold far differently than a conversation about education in East Broadway. “On education, there’s a lot of concern around school assignment because a lot of underperforming schools are in these communities,” he says. “We’re talking about strengthening every school in the city. I’m very comfortable campaigning in general, extremely comfortable in communities of color. My district is more than half people of color. For those people who don’t know me, growing up here helps. I’m more comfortable in Dudley Square than at a table of executives downtown.”

Connolly, meanwhile, has made a point of making frequent campaign stops in Roxbury lately. He has lined up support among neighborhood clergy, including some who had been sharply critical of his handling of education issues in the past. And he’s thrown himself into retail politicking in neighborhoods that largely shunned him during September’s preliminary election. He darted in and out of barber shops, beauty salons, and restaurants during one recent walk through Grove Hall, shaking hands, asking questions, and promising to bring a booming downtown business scene into a neighborhood pockmarked by empty storefronts.

Connolly’s recent Grove Hall walk was aimed at rolling out initiatives supporting minority- and women-owned businesses. But after making his pitch for a Roxbury-based entrepreneurship incubator and a small business venture capital fund and municipal control over restaurant liquor licenses, the talk invariably turns to education. That’s a topic Connolly has been hammering away at since jumping into the mayoral race early this year.

“A stronger economy requires better schools, better opportunities for adults and children, and safer neighborhoods require the same thing,” Connolly says. “When you talk about schools, you’re invariably talking about safe and healthy neighborhoods. Talk to people who’re really impacted, they know that.” He argues that his campaign’s focus on education “resonates across the city,” and he credits the citywide impact of education issues with pushing him through to November’s final. “I spent six years on the city council talking about schools, and a lot of that time was spent in communities of color. We’re going to build off all that work. The only change is the final leaves you with two choices.”