iOS and Android both have garbage collection, and it is mandatory for neither OS. (I would consider ARC garbage collection, and nothing is stopping you from running C code on Android.)
Android has garbage collection, yes.
Since iOS5 there's refcounting available, but that's far away from garbage collection. Just add some circular dependencies and refcounting will fail. And no, that's not only a theoretical problem (as everyone who used Python's refcounting before version 2 can tell you).
It is irrelevant to cite situations under which an algorithm will fail to reclaim storage as evidence that an algorithm is "not garbage collection", since it is provable that situations exist for every possible algorithm. I can write a program that creates an infinite linked list but only ever uses the head, most GCs would fail to reclaim the tail of the list even though it is garbage.
This is not a theoretical concern, space leaks are possible under any automatic storage reclamation scheme.
Since in practice you can write applications for Android and iOS with languages and runtimes of your choice...
As you must know, the very name Garbage Collection implies an asynchronous process that travels up and down the program memory street at periodic intervals, trying to find garbage to collect.
The iOS model is more like a waiter in an expensive restaurant who comes and takes your plate away the instant the last morsel of food is in your mouth. You don't have to discard the plate yourself, but you can guarantee he will pick up your plate the moment its free to be picked up.
Actually, that's not true.
Since at least NeXTSTEP there's refcounting. In 1989, NeXTSTEP introduced their NSObject-based Objective-C runtime with relied on -retain and -release calls to count object references. I can only find records commenting on NSObject's support for -retain and -release, but it may have been done earlier in a different Objective-C based runtime. (And I'm certain refcounting was pioneered in earlier runtimes.)
In 1995, the OpenStep standard introduced autorelease pools, which helped automate reference counting. Calling -autorelease on an object increments the retain count and instructs the enclosing autorelease pool to decrement the count when it pops.
In 2011, Lion and iOS 5 introduced ARC – Automatic Reference Counting. It's actually a pretty sweet memory management solution where simple statically applied code transformations streamline memory management without the need of a garbage collector. As you note though, circular dependencies cannot (yet!) be handled by ARC. To assert that circular dependencies can only be handled through garbage collectors is possibly short-sighted. I know the team that implemented ARC already has prototypes that handle some kinds of circular dependencies, or warn programmers of possible circular deps in their code.
To say automatic ref counting is "far away" from garbage collection is rather disingenuous. It's simply different. Both have tradeoffs. Garbage collection handles all memory management for you; automatic reference counting still requires some manual memory management. GC gracefully deals with circular dependencies; ARC leaks memory with circular dependencies. GC requires runtime overhead in memory and clock cycles; ARC minimizes memory and CPU overhead and, when you need zero overhead, you can drop down to manual memory management.
Frankly, I far prefer ARC to GC. ARC gives me almost all the benefits with no runtime overhead. There's nothing running alongside my code that might randomly suck up cycles or pause execution, and I can always profile exactly what my users will run. Don't knock refcounting just because it's not vogue.
My point about profiling the exact user experience still stands. I can exactly instrument the hotspots in my code and fix them as needed – I can disable ARC, I can avoid autorelease pools. (Or I can add my own autorelease pools or manual retains, preventing large objects from being freed until I'm outside of a hotspot.) Importantly, I know what's being profiled is exactly what will be run by my users. I can't say the same about GC code, since the collector must be free to reap whenever and however it decides. Heck, depending on the runtime, I can't even be certain which GC algorithm will be used by my customers.
I appreciate the control refcounting gives me, and I love that ARC makes writing refcounted code almost as painless as writing GC code without the loss of control. I like being able to test and profile exactly what my users will run.
It's not, so you should not, because that's completely wrong.