We combine linear viscoelastic measurements and modeling in order to explore the dynamics of blends of the same-molecular-weight ring and linear polymers in the regime of the low volume fraction (0.3 or lower) of the ring component. The stress relaxation modulus is affected by the constraint release (CR) of both rings and linear components because of the motion of linear chains. We develop a CR-based model of ring-linear blends which predicts the stress relaxation function in the low fraction regime of the ring component in excellent agreement with experiments. Rings trapped by their entanglements with linear chains can only relax by linear-chain-induced CR, with much slower relaxation of rings compared to linear chains. The relative viscosity eta(phi(R)*)eta(L) of the blend with respect to the linear melt viscosity eta(L) at a ring overlap volume fraction phi(R)* is predicted to increase proportionally to the square root of the ring molecular weight root M-w,M- R. Our experimental results clearly demonstrate that it is possible to enhance the viscosity and simultaneously the structural relaxation time of linear polymer melts by adding a small fraction of ring polymers. These results not only provide fundamental insights into the physics of the CR process but also suggest ways to fine-tune the flow properties of linear polymers by means of adding rings.