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In the Bank of America Trends in Consumer Mobility report, released Monday, surveyors asked 1,000 adults about the importance of various items in their daily lives. Among millennials, 93 percent said a smartphone was "very" or "somewhat" important, making it the most important item for that age group. Fewer—87 percent—said deodorant was of daily importance, and 91 percent, a toothbrush.

Millennials are famously unemployed and underemployed, but the reason may not entirely be the so-so job market. Or gaps in their college education.

It's a departure from older generations. Among all adults surveyed, deodorant and smartphones were deemed equally important in daily life, at 91 percent, while the toothbrush got top ranking, with 95 percent saying it's a daily must.

That differential stinks for grads' employment prospects.

"Research on first impressions shows people look at not just how you comport yourself, but how you present yourself," said Susan RoAne, author of "How to Work a Room." Advice on job interviews often emphasizes presentable clothes and a trim haircut, but fresh breath and a clean scent are must-haves, too. (She also tells attendees of her networking presentations to skip odorous foods like onions and garlic before important interactions.)

"If people can smell you before they see you, you aren't getting the job," said RoAne. Slip into bad hygiene habits after getting hired, and you're not likely to get promoted, or last in a position that involves face-to-face contact with executives or clients.

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Grads already face a tough market. In May, the latest data available, unemployment among 25-to 34-year-olds was 6.7 percent, up slightly from 6.6 percent in April. Unemployment in the 20-24 age group was 11.1 percent, up from 10.6 percent. To compare, unemployment for all adults age 20 and older is 5.8 percent.

Part of the problem might be that some grads aren't really trying to get hired, said Steve Tobak, managing partner of Invisor Consulting, a management strategy consulting firm based in Silicon Valley.

"What entrepreneurialism is for many of them is hanging out in their parents' basement or their childhood bedroom with their smartphone, calling themselves the CEO of this one-person company," said Tobak. "It's sad, but you don't need personal hygiene when you're the only person in the business."

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Neither is it really the best strategy. Even if starting your own business is the right call, ultimately, most grads would still benefit from a little real-world work experience before striking out on their own, he said.

"Experience is the best teacher," Tobak said. "But buy some deodorant before you get out there."

—By CNBC's Kelli B. Grant