Chains of Love

You report the theft to the concierge who, after he finishes laughing, demands that you vacate your room immediately, since you cannot pay for a longer stay.

"Well I'll simply wire my family for the funds," you reply.

"Ha-ha!" the ever-jovial concierge continues, "This week is fête week in Puzzlania- all businesses except hotels and bars are closed. You won't be able to receive any money for seven days. Since it is hotel policy to not extend credit, you'll have to leave."

In desperation, you search your pockets for some form of currency. At last you realize you are wearing a precious solid-gold bracelet given to you by your long-lost love.

"Here, this gold bracelet has seven links. Each link is easily worth enough to pay for a night in your hotel."

After examining in the bracelet he replies, "Fine. I'll take the bracelet as collateral until you can pay in full."

Already severely unimpressed with his manners, and now beginning to suspect he might have had a hand in the disappearance of the rest of your belongings you pause, "No. I'll only let you have as much collateral as you are due on any given day. Today you may have one link, tomorrow two, the next day three, until the week is up when you'll have all seven. Then I will return to pay in full and retrieve my bracelet."

This agreed to, you prepare to cut the bracelet. Considering its high emotional-value, you want to do as little damage as possible so it may be easily repaired. What is the fewest number of cuts you can make so the hotel may hold onto all the collateral they need, but no more?