Help with question involving k-regular graphs In my last test, our teacher gave us this question:


  In an conference with 90 participants, the staff wants to divide all
  participants in 6 groups of 15 participants each. Each participant of
  each group must have at least one article with exactly 7 other
  participants of the same group. Prove using Graph Theory that this
  division is impossible.


I spent a lot of time thinking about, but couldn't find an definitive answer. I think that this involve bipartite matching somehow, but I have no idea on how to proceed with the proof. I thought that maybe creating a k-regular graph would prove that this don't have a matching, but I couldn't come with the graph representing the problem.

Can I get some help with this?
There is no 7-regular graph on 15 vertices, since $7\times 15$ is odd.