Could a relativistic rocket use elliptical orbits for faster deceleration and acceleration? 
The biggest hurdle with relativistic rockets seems to be their acceleration and deceleration times. If 1 g propulsion were possible, it would still take over a year to get up to relativistic speeds, more years for the journey, and more years slowing down. If the ship wanted to make a second trip, it would take more years to accelerate again.
But if the relativistic rocket were in an elliptical orbit around a star, could a smaller vessel deploy from the larger at the slowest arc of the elliptical orbit, visit any planets in the system, and then return to the larger vessel when it's back at its slowest arc, before slingshotting out of the system at the same relativistic speed it entered?
Ideally, the free fall would enable the ship to accelerate and decelerate without experiencing adverse G forces, so that it would no longer take years to decelerate and accelerate for each star it stops at.
 A: Relativistic speeds are vastly greater than orbital speeds around stars. For exxample, Earth's orbital speed is about 30 km/s, or about .00001c. Nothing moving at relativistic velocity could stay in orbit around an ordinary star. The only bodies for which orbital speeds are relativistic are black holes. For those there might be the possibility of relativistic slingshot paths close to the event horizon. I would guess that tidal forces would pose a significant hazard though, not to mention radiation from the accretion disk.
A: I see a lot of problems with this approach. At first, not all planets orbits will cross nearby a lowest arc speed section of a rocket. Second, even if they would - it does not mean that given planet X speed will be lowest at that position. So it's clear that it's impossible to optimize one path for all planets. For some, it may require a considerable thrust adjustment, so additional fuel consumption. Flight trajectories are best optimized when exact target planet is known, so specific gravitational pulls from specific planets can be exploited then. No one size which fits all.
