SpaceX Interplanetary Transport System: https://www.youtube.com/watch?v=0qo78R_yYFA
The rocket looks very large and they mention 120 million newtons takeoff thrust so the weight is about 10 million kg, 3 times Saturn V size.
The first stage lands back on launch stool, the tanker stage is put on top of it and it launches again. This implies a relatively fast turnaround.
Both the second stage and the tanker seem to have complete heat shields and stub wings and ability to re-enter either Mars or Earth.
So all parts
1) big
2) landable and
3) short turnaround time
I don't understand the 100 000 km/h which is 30 km/s speed for the Mars cruise. Would be really hard to achieve with chemical propulsion. With 4 km/s exhaust velocity and delta vee of say 20 km/s you get a required mass ratio of e^(20/4) which is 150. And they lug the upper stage engines all the way, and there's heatshield and wings. Impossible.
Also the 200 kW electrical power advertised is puny for electrical propulsion. With an ISP of 1000 (exhaust 10 km/s) you get an 20 Newtons of thrust [correction from 200N], which is nothing for their ship size. If they only have ten tons of mass, then it takes 200 days to accelerate to full speed.
Typically you might need 10 to 20 km/s speed for Mars.
Their plan does not compute for me.
EDIT: So it can work if they only go for 10 km/s.
They massively oversize the second stage and launch it almost empty, so it can just do the 5 km/s or whatever is needed for orbit. Then they launch multiple tankers to refuel it.
They don't need lots of engines on the second stage because it's launched light.
So it's pure chemical propulsion.
But still with only 4 km/s exhaust velocity, no matter how you slice it, the mass ratios required from a single stage get impossible, ie even if the rocket tanks and engines didn't have any mass, payload sets an upper limit to the mass ratio.
EDIT: So looks like it has 10 km/s delta vee. Not 30.
Most of it, you would get for free, since the ship is launched from the Earth, which is already moving at ~30 km/s. The delta-v cost is much less then that.
I am very curious what the selected family of orbits is, and even more importantly how long & how much life support for the large passenger number.
There's not much leeway, it's going to be something close to a Hohmann transfer, with the aphelion ahead of and above Mars to get to a hyperbolic capture orbit with the periareion deep in the atmosphere for (almost) direct re-entry.
This kind of orbits can be solved for arbitrary departure date and time of flight using a Lambert's problem solver and numerical optimization. Not a particularly difficult problem by modern standards.
Pure Hohmann transfer to another planet will result in inevitable collision due to relative velocity, but it's useful for lower bound estimates.
Another alternative for recurring Mars intercept is is the "Aldrin cycler" (after Buzz Aldrin) which is a free return trajectory but that is difficult when the goal is to land and take off again.
There are lots of possibilities for lower energy transfers but most of them are out of question when life support is required for humans on board.
A pure ion drive for all the equipment even if this means it takes 4x as long to get there, then a 'small' capsule back and forth for people.
Basically you need at least 10 kW per Newton.
The other option, is to have a pure transit vehicle from earth orbit to mars orbit and then a 3rd vehicle to land with. This, would work really well if we wanted to really colonize mars. But, if your only sending say 10 people the R&D is not worth the fuel savings.
PS: Let's say it's a 20,000 lbs craft or ~1/10th of the shuttle and your getting ~8.8 N or 1 lbs of thrust for 120 days. That's 9.8 m/s / 20,000 * 60 * 60 * 24 * 120 = 5k m/s. If you already need the panels while in mars orbit, that seems like a no brainier. Finally, If that's 200kw in mars orbit then the numbers seem even more reasonable as that's 460 kw near earth and the extra 260kw ~= 26 newtons which could add ~5km/s to a 60,000 lb spacecraft.
Maybe for course corrections where you need to fine tune the orbit a couple of mm/s here and there?
For unmanned missions it does make good sense as the mass doesn't grow so strongly if the trip time gets longer.
Thinking about that I think I figured it out. The earth is going 30 km/sec around the sun, so that's probably where the 30 km/sec comes from. 30 km/sec is well past single stage to orbit and they would not need a booster if they could get into that range.
Mars is doing 50km/sec around the sun, but you can cheat in a few places as your earth orbit can add ~8km /sec from orbiting around earth. That's 50 - 30 - 8 ~= 12km/s plus delta V get out of suns and earths gravity well. But you can also play with orbital mechanics to save some energy and you can also subtract the orbital velocity around mars.
Anyway, I am not sure how much delta V you need, but it's well under 30km/sec.
PS: Video had refueling in what looked like LEO, but if your in a higher orbit the craft needs less fuel to get to Mars from that orbit.
With traditional rockets you can accelerate, get a gravity assist boost and save enough fuel to slow down quickly when you are at the orbital insertion point.
For example, Mars Science Laboratory did the same, and it didn't need to spend fuel trying to enter orbit.
http://mars.nasa.gov/msl/mission/timeline/approach/
The closing velocity of spacecraft and Mars is nowhere near 25 km/s.
As another example, Apollo did a direct entry to Earth as well.
Even when entering orbit, you can sometimes use aerobraking or aerocapture, though it's either limited in delta vee or dangerous if you go lower.