1 A quiz team must answer questions from six different topics, numbered 1 to 6. The team has six players, \(A , B , C , D , E\) and \(F\). Each player can only answer questions on one of the topics. The players list their preferred topics. The bipartite graph shows their choices.
\includegraphics[max width=\textwidth, alt={}, center]{f5890e58-38c3-413c-8762-6f80ce6dcec7-02_711_499_781_760} Initially, \(A\) is allocated topic 2, \(B\) is allocated topic \(3 , C\) is allocated topic 1 and \(F\) is allocated topic 4. By using an alternating path algorithm from this initial matching, find a complete matching.
[0pt] [5 marks]