Create set with exclusion rules from a dataframe

I would like to create groups from my data frame. Teams with 1 in the corresponding row/column cannot stay in the same group.

How to create the largest groups and fond the minimum number of groups?

Idea

There are 5 teams (50 in the original dataframe) for some reason some teams have players in common. The data frame shows with 1 if two teams have a player in common if not, the cell is filled with nan. How many and which teams can play together at the same time?

Here a sample data frame

pd.DataFrame.from_dict(data={'team1': [np.nan,1.0,1.0,np.nan,np.nan],
                   'team2':[1.0,np.nan,np.nan,np.nan,np.nan],
                   'team3':[1.0,np.nan,np.nan,np.nan,1.0],
                   'team4':[np.nan,np.nan,np.nan,np.nan,np.nan],
                   'team5':[np.nan,np.nan,1.0,np.nan,np.nan]}, orient='index',
                      columns=['team1', 'team2', 'team3', 'team4', 'team5'])

	team1	team2	team3	team4	team5
team1	NaN	1.0	1.0	NaN	NaN
team2	1.0	NaN	NaN	NaN	NaN
team3	1.0	NaN	NaN	NaN	1.0
team4	NaN	NaN	NaN	NaN	NaN
team5	NaN	NaN	1.0	NaN	NaN

Expected output

In this easy case the minimum number pf groups is 2, and the possible solution is:

group1 = ['team1', 'team4', 'team5']
group2 = ['team2', 'team3']

from Create set with exclusion rules from a dataframe