If we consider one division and internal games only, then each vertex (team) has a degree 9. However, by the Handshaking lemma, the sum of degrees over all vertices must be even.
In a league with two divisions of 13 teams each, determine whether it is possible to
schedule a season with each team playing nine games against teams within its division and four games against teams in the other division.
Please help... Thanks!
If we consider one division and internal games only, then each vertex (team) has a degree 9. However, by the Handshaking lemma, the sum of degrees over all vertices must be even.