There used to be 26 football teams in the National Football
League with 13 teams in each of two conferences. An NFL guideline
said that each teams's 14-game scedule should include exactly 11 games
against teams in its own conference and 3 games against teams in the
other conference. Describe a graph model for this. Look at
the subgraph for one conference and explain why this guideline could
not be satisfied.
Suppose all of the vertices of a graph G have degree n, where n
is an odd number. Show that n must divide the number of edges in
G.