Write a Mathematical report which includes mathematical notation in line with graph theory for Q$3$ The games now need to be scheduled, which will happen in two steps. Your first task is to group

together games that can be played simultaneously into game groups. The requirements for the game

groups are:

People are not double$-$booked: each person is involved in at most one game in any game group.,

either as a player or referee

Games are played once: each game is in exactly one game group

Each game group will be played in a single time slot, so the committee wants the smallest number of

game groups possible.

Implement your solution as a Python function of the form

def gameGroups$($assignedReferees$)$:

where assignedReferees is in the same format as you returned in the previous question, i$.$e$.$ as a

dictionary with games as keys and referees as values. Your output should be a schedule in a data

structure of the form