  Polymers are an effective test-bed for studying topological constraints in
condensed matter due to a wide array of synthetically-available chain
topologies. When linear and ring polymers are blended together, emergent
rheological properties are observed as the blend can be more viscous than
either of the individual components. This emergent behavior arises since
ring-linear blends can form long-lived topological constraints as the linear
polymers thread the ring polymers. Here, we demonstrate how the Gauss linking
integral can be used to efficiently evaluate the relaxation of topological
constraints in ring-linear polymer blends. For majority-linear blends, the
relaxation rate of topological constraints depends primarily on reptation of
the linear polymers, resulting in the diffusive time $\tau_{d,R}$ for rings of
length $N_R$ blended with linear chains of length $N_l$ to scale as
$\tau_{d,R}\sim N_R^2N_L^{3.4}$.
