So I have a seemingly basic problem, but the wording is vague to me so I was wondering if anyone could give any assistance.
The problem:
There used to be 26 football teams in the NFL with 13 teams in each of two conferences. An NFL guideline said that each team's 14 game schedule should include exactly 11 games against teams in its own conference and 3 games against teams in the other conference. By considering the right part of a graph model of this scheduling problem, show that this guideline could not be satisfied!
I picked out the information, and deduced that the number of vertices was 26, with the degree of each vertice being 14 (since each team plays 14 games). Using the theorem that states
In any graph, the sum of the degrees of all vertices is equal to twice the number of edges,
I found the number of edges to be 182. I'm really not sure what this signifies, or if I even did this correctly. Maybe having just looked a single conference would've steered me more in the right direction (if I'm off it)?
Hint: Look at the games the teams played in their own conference. Each of $13$ teams played exactly $11$ others. This means that the total number of games played in the conference should be $\frac{11(13)}{2}$, but wait... that seems fishy.