Given the 1/3rd of Earth's gravity on Mars and neglecting space suit limitations and also assuming you have maintained your muscle strength, would you run faster on Mars?
The answer may not be so straightforward.
This is similar to the reduced 1/6th gravity on moon compared to the 1/3rd on Mars. We all have seen the video footage from the moon landings and walks on the moon surface. The astronauts appear to have increased foot strength but they have in a rather slow general movement, especially evident when they are waving their hands. This is maybe because absent or reduced gravity (microgravity) makes you actually float like inside water. Your limbs' muscles are constantly fighting your own mass's inertia
(buoyancy replaced by the word inertia) and your feet maybe stay longer on "air" not touching the ground since you are not assisted by the Earth's gravity increased downward force. So I guess this is an open question.
image source: https://www.pinterest.com/pin/763078730595604862/
Update 7 May 2022: Seems this question has risen quite a debate in the last couple of days. I did some more digging in the literature and could find only one directly dedicated publication to this question about running on Mars:
https://pubmed.ncbi.nlm.nih.gov/15856558/ (Abstract only)
Also about running on the moon this research here says that experiments have shown that the maximum speeds achieved will be much greater than initially theoretical predicted mainly due to the extra momentum gained by the hands movement, but still inferior speeds to Earth's gravity:
Best Answer
The speed of walking and running depend on pendulum-like motion of the legs. If you walk at different speeds the power used varies, and has a minimum roughly corresponding to the free pendulum motion of your legs.
That swing time is $T\approx 2\pi \sqrt{L/g}$, and since each step has a length proportional to your leg length $L$ the speed scales as $v\propto L/T = \sqrt{gL}$. So you will tend to walk more slowly in low gravity. This is complicated by people talking longer steps in lower gravity. This can be tested using parabolic flight or having weight-reducing spring suspensions.
However, running involves moments when both legs are in the air. It becomes energetically favourable for bipeds when the Froude number is $\approx 0.5$, or $v=\sqrt{g L/2}$. So at lower gravity you start running at lower speeds, which also checks out with suspended runners. The energetically most favourable speed is at Froude = 1/4, which means you will tend to run at a speed scaling as $\sqrt{g}$. So Martian runners would tend to run at about 60% of Earth runner speeds.
Low gravity running also involves a flatter trajectory with less bouncing, and has a reduced energy cost compared to walking: on Mars people may be running more, but do it more slowly.