For a tournament with 8 vertices, if from any vertex it is impossible to follow a route to return to itself, we call the graph a good graph. Otherwise, we call it a bad graph. Prove that
(1) there exists a tournament with 8 vertices such that after changing the orientation of any at most 7 edges of the tournament, the graph is always abad graph;
(2) for any tournament with 8 vertices, one can change the orientation of at most 8 edges of the tournament to get a good graph.
(A tournament is a complete graph with directed edges.) combinatoricsgraph theory