Can I keep my hair healthy if I just wash it once a month?

Many homeless men seem to have long hair and rarely shampoo, but we do accumulate dirt and air pollutants on our hair from living in the city. Shampooing daily or every other day keeps the hair clean. For me, I like a clean hair and scalp and would personally feel bad if I started to develop an odor in my hair, which is common in people who do not wash it.