Round robin scheduling requirement: Games Per Team Total

I’m new to round robin scheduling and stuck on this requirement where we pass in the Teams array and minimum number of matches a team should play. I’ve implemented single and double round robin algorithm such as:

teams = [‘T1’, ‘T2’, ‘T3’, ‘T4’];

Single round robin generates this:

T3 vs T2
T4 vs T1
T2 vs T4
T3 vs T1
T1 vs T2
T3 vs T4

Double Round Robin Generates This:

e.g

count = len(teams)
adjusted_count = count - 1 if count % 2 == 0 else count
total_matches = adjusted_count * 2

T3 vs T4
T1 vs T2
T4 vs T1
T3 vs T2
T2 vs T4
T3 vs T1
T4 vs T3
T2 vs T1
T1 vs T4
T2 vs T3
T4 vs T2
T1 vs T3

Now, requirement is such as: I pass teams arra, I set number of minimum matches that each team should always play, e.g 4 Teams, Min matches per team total =3

How do I implement that?

My Code:

import random

def rotate(lst):
    return lst[1:] + lst[:1]

def make_schedule(teams, rounds=None, shuffle=True, seed=None):
    team_count = len(teams)
    
    if team_count < 2:
        return []
    
    # Account for odd number of teams by adding a bye
    if team_count % 2 == 1:
        teams.append(None)
        team_count += 1

    if shuffle:
        # Seed shuffle with seed or randomize if seed is None
        random.seed(seed)
        random.shuffle(teams)
    elif seed is not None:
        # Generate friendly notice that seed is set but shuffle is set to false
        raise ValueError("Seed parameter has no effect when shuffle parameter is set to False")
    
    half_team_count = team_count // 2
    
    if rounds is None:
        rounds = team_count - 1

    schedule = []
    for round in range(1, rounds + 1):
        round_matches = []
        for key in range(half_team_count):
            team1 = teams[key]
            team2 = teams[key + half_team_count]
            # Home-away swapping
            matchup = [team1, team2] if round % 2 == 1 else [team2, team1]
            round_matches.append(matchup)
        
        schedule.append(round_matches)
        teams = rotate(teams)
    
    return schedule