Ruthenbeck took over at the Bundesliga's bottom club following the departure of Peter Stoger.
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A Robert Lewandowski goal ended the resistance of rock bottom Cologne as Bayern Munich extended their Bundesliga lead to nine points with a 1-0 win.
Two penalties in the final minutes of the match saw winless Cologne capitulate as they threw away a 3-0 lead to lose 4-3 at home to Freiburg.
Cologne appointed former Stuttgart and Eintracht Frankfurt coach Armin Veh as managing director on Wednesday.
The club, who qualified for the Europa League last season, have drawn three and lost 11 of their league matches.
Restricted to just four appearances for Cologne, veteran striker Claudio Pizarro has apparently found a part-time job to keep himself busy.
Gunners finished first as Red Star Belgrade and BATE Borisov could only draw 0-0 in group's other game.
Cologne have announced that their all-time record goal scorer Hans Schafer, who won the 1954 World Cup with West Germany, has died at the age of 90.
Cologne have announced that they will appeal UEFA's punishment imposed on them for fan misconduct in the Europa League match at Arsenal in September.
Cologne have been ordered to pay a settlement to Arsenal over damage caused by their supporters during the Europa League tie at the Emirates.
Struggling Cologne has parted company with managing director Joerg Schmadtke after the side's winless start to the Bundesliga.
Cologne have signed free agent Claudio Pizarro on a contract until the end of the season.
A UEFA inspector will seek answers from Arsenal and Cologne over the cause of the crowd trouble that marred last week's Europa League meeting.
Cologne will not demand that their 5-0 defeat at Borussia Dortmund is replayed, the Bundesliga club announced on Tuesday.
Cologne want to force a rematch after an irregular goal was wrongfully awarded in their 5-0 loss to Borussia Dortmund on Sunday.
Braces from Maximilian Philipp and Pierre-Emerick Aubameyang ensured Dortmund went to the top of the Bundesliga table as they beat Cologne 5-0.