Your college has sent a contingent to take part in a cultural festival at a neighbouring institution. Several team events are part of the programme. Each event takes place through the day with many elimination rounds. Your contingent is multi-talented and each individual has the skills to take part in a subset of the events. However, the same individual cannot be part of the team for two different events because of a possible clash in timings. Your aim is to create teams to take part in as many events as possible.
To do this, you decide to model the problem as a graph where the nodes are the events and edges represent pairs of events where the team that you plan to send shares a member. In this setting, the graph theoretic question to be answered is: