$($COMPUTER SCIENCE$)$

Alice wants to throw a party and she is trying to decide who to invite. She

has n people to choose from, and she knows which pairs of these people

know each other. She wants to invite as many people as possible, subject to

two constraints:

For each guest, there should be at least five other guests that they already

know.

For each guest, there should be at least five other guests that they don't

already know.

Describe and analyze an algorithm that computes the largest possible number and Prove$($Show the proof$)$ or disprove justifying why a greedy approach works or does not work

of guests Alice can invite, given a list of n people and the list of pairs who

know each other.