If you have a small solar panel, you probably don't have to worry about limiting the charge current (as the battery will be able to handle more that the solar panel can supply).

So the only thing left to do is prevent over-charge (i.e. disconnect the solar panel is the voltage on the battery goes above 4.2V. But protected cell can do this for you. I'm not knowledgeable enough to know if it's a good idea to rely on this.

Also make sure the solar panel isn't connected when it's dark, as the solor panel will use current when it's not generating it. Though a simple diode will do this trick. But you'd get a 0.6V drop on the diode, so you might want to get some extra efficiency by detecting output and switching the solar panel using the Arduino.

The last problem is overdischarge, unless you have a protected cell. But that's a problem you have, even without the charging bit.

If you have a small solar panel, you probably don't have to worry about limiting the charge current (as the battery will be able to handle more that the solar panel can supply).

So the only thing left to do is prevent over-charge (i.e. disconnect the solar panel if the voltage on the battery goes above 4.2V). Protected cell can do this for you. I'm not knowledgeable enough to know if it's a good idea to rely on this.

Also make sure the solar panel isn't connected when it's dark, as the solor panel will use current when it's not generating it. Though a simple diode will do this trick. But you'd get a 0.6V drop on the diode, so you might want to get some extra efficiency by detecting output and switching the solar panel using the Arduino.

The last problem is overdischarge, unless you have a protected cell. But that's a problem you have, even without the charging bit.