Message from IA Gunther van den Bergh
Attached find FIDE Laws.
Basically, G4 rule works as follows:
1. Player has less than 2 minutes on the clock and claims G4 (which is also an offer of a draw).
2. If the opponent accepts then the game is drawn.
3. If the opponent rejects the offer, the arbiter intervenes.
4. The arbiter must establish why the player is making the claim.
5. If the arbiter agrees, he adjusts the clocks.
6. If the arbiter rejects the claim, the players continue playing.