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.

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