| Correct (1) | Missing or very wrong (0) | ||
|---|---|---|---|
| Chromatic number | Number is explicitly stated and correct. | The number is wrong, missing, or given only implicitly via the upper/lower bound arguments. | |
| Correct (3) | Buggy (2) | Missing or Wrong (0) | |
| Upper bound argument | A correct coloring is presented separately from the lower bound argument. Any mistakes are minor and do not affect the chromatic number. | Coloring has a small mistake that changes the chromatic number. | Coloring has major or multiple mistakes. Very wordy presentation (e.g. step by step process). Coloring is missing or given only implicitly via the lower bound argument. |
| Correct (3) | Buggy (2) | Missing or Wrong (0) | |
| Lower bound argument | An appropriate special subgraph is identified and located, or a clear and convincing step-by-step coloring is given. | An appropriate subgraph is named but its location isn't clearly described. A correct step-by-step coloring is used but it is wordy or hard to follow. | Lower bound argument is missing, very hard to understand, or supports a value smaller than the true chromatic number. |
| Correct (2) | Buggy (1) | Missing or very wrong (0) | |
|---|---|---|---|
| Start of proof | Proof begins with correctly negated claim. | Small mistakes in negation which have limited impact on the rest of the proof. | Mistakes in negation that are major or have major impacts on proof. |
| Correct (1) | Missing or wrong (0) | ||
| Final contradiction | Ends with a contradiction or obviously false fact. | Contradiction is missing or not actually a contradiction or merely repeats part of the negated claim. | |
| Correct (3) | Buggy (2) | Missing or wrong (0) | |
| Flow | Proof proceeds in a reasonably direct way from the negation to the contradiction. Steps are in logical order. | Proof connects the start to the end but takes small detours, has some scratch work mixed in, or is somewhat too long. Proof is based on an incorrect negation that significantly simplified the argument. | The logical steps from negation to contradiction are unclear, missing, excessively long, or have serious mathematical flaws. The main argument is circular, backwards or disconnected from the initial negation. |
| Correct (3) | Buggy (2) | Missing or very wrong (0) | |
| Style, clarity, details | Easy to follow, with appropriate use of punctuation, notation, latex, and whitespace. Algebra, variable declarations, and use of definitions is correct or nearly so. | Slightly hard to follow. Small number of minor mistakes e.g. formatting bugs, algebra mistakes, too few steps or key steps not explained. | Hard to follow or looks unprofessional. Serious or multiple technical issues. |