Chromosomes in living cells are strongly confined but show a high level of spatial organization. Similarly, confined polymers display intriguing organizational and segregational properties. Here, we discuss how ring topology influences self-avoiding polymers confined in a cylindrical space, i.e. individual polymers as well as the way they interact. Our molecular dynamics simulations suggest that a ring polymer can be viewed as a “parallel connection” of two linear subchains, each trapped in a narrower imaginary tube. As a consequence, ring topology “stiffens” individual chains about fivefold and enhances their segregation appreciably, as if it induces extra linear ordering. Using a “renormalized” Flory approach, we show how ring topology influences individual chains in the long chain limit. Our polymer model quantitatively explains the long-standing observations of chromosome organization and segregation in E. coli.