She returned to Johns Hopkins for graduate work, and completed her dissertation on "absolute reducibility of maps of at most 19 regions" in 1966 at the age of 47. Bari's dissertation explored chromatic polynomials and the Birkhoff–Lewis conjecture. She determined that, "because of the fact that all other cubic maps with fewer than 20 regions contain at least one absolutely reducible configuration, it follows that the Birkhoff-Lewis conjecture holds for all maps with fewer than 20 regions."Bari, Ruth. Abstract: “Absolute Reducibility of Maps of at Most 19 Regions.” Biographies of Women Mathematicians Her Ph.D. advisor was Daniel Clark Lewis, Jr. and her thesis was titled, Absolute Reducibility of Maps of at Most 19 Regions.
