# Graph Theory questions

**In a league with two divisions of 13 teams each, no schedule has ****each team playing exactly nine games against teams in its own division and ****four games against teams in the other division.**

**ANSWER :** If this were possible, then we could form a graph with the teams as vertices, making two vertices adjacent if those teams play a game in the schedule. We are asking for the subgraph induced by the 13 teams in a single division to be 9-regular.

However, there is no regular graph of odd degree with an odd number of vertices, since for every graph the sum of the degrees is even.