It is a homework question from a introductory graph theory course.
- Amongst a dinner party for ten people each person has at least five friends attending. Prove that the group can be seated around a table so that everyone has a friend sitting on either side of them.
- This time suppose that each of the group of ten has only four friends attending. Prove that a similar seating arrangement is not always possible.
- What if two of the group have only four friends attending and the rest at least five each?
- Four with four friends , the rest at least five each.
I have no idea how to do it. Could anyone help me?