Bonus
The discharging method was introduced to prove Wernicke’s (“VER-nick-uh’s”) theorem, which bounds the degrees of vertices in graphs with this property. For 10 points each:
[10m] Name this property that a graph has if and only if it does not contain the subgraphs K-five or K-three-three.
ANSWER: planar [accept planarity or being planar or planar graphs]
[10h] A graph is planar if and only if its value for this number is zero. The Albertson conjecture links the chromatic number of complete graphs to this number, which a formula by Richard Guy gives a potential upper bound on for complete graphs.
ANSWER: crossing number
[10e] The complete graph with n vertices has a circuit named for this mathematician if and only if n is odd. This mathematician created graph theory to solve the Seven Bridge of Königsberg problem.
ANSWER: Leonhard Euler [accept Eulerian circuit]
<Other Science>
Answerlines and category may not exactly match the version played at all sites
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Cornell A | North Carolina A | 0 | 0 | 10 | 10 | E |
Summary
| Tournament | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|
| 2025 ACF Nationals | Yes | 1 | 10.00 | 100% | 0% | 0% |