13. There are 12 teams participating in a single round-robin invitational tournament, where each team plays exactly one match against each of the other 11 teams. In each match, the winning team gets 2 points, the losing team gets 0 points, and in the case of a draw, both teams get 1 point. Which of the following statements about the points scored by the 12 teams is incorrect?
(A) The number of teams with an odd number of points must be even.
(B) The number of teams with an even number of points must be even.
(C) It is impossible for two teams to score 0 points.
(D) The total points scored by all teams is no less than 100 points.
(E) The highest score of any team is no less than 12 points.
13. E.

It is clear that options $\mathrm{A}$ and $\mathrm{B}$ are both possible;
Among the 12 teams, since the two teams with the lowest scores must play a match, one of them must gain points, so it is impossible for two teams to both have 0 points, thus eliminating option $\mathrm{C}$;
The 12 teams play a total of $\mathrm{C}_{12}^{2}=66$ matches, with each match contributing a total of 2 points, so the total score sum is
$$
2 \mathrm{C}_{12}^{2}=2 \times 66=132>100 \text{. }
$$

Thus, option D is eliminated;
If all teams draw, each team will have 11 points, which contradicts the requirement that the highest score must be at least 12 points, making it incorrect. Therefore, the correct choice is E.