There are many asteroids that actually cross the orbital path of Earth - once on the inbound and once on the outbound leg of each of their elliptical orbits. The same asteroids normally also cross the orbital path or Mars.
We know that it takes a huge amount of fuel to propel a spacecraft to achieve escape velocity from Earth and then additionally, provide it with enough kinetic energy to 'climb', relative to the Sun, to the orbital distance of Mars.
Can an Earth-Mars mission save propulsion energy by somehow 'hitching a ride' on an asteroid that crosses the orbital paths of Earth and Mars?