Every graph with no K_t minor is (t-1)-colorable.
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Statement
For every $t \ge 1$, every graph with no $K_t$ minor has chromatic number at most $t-1$.
Assessment
Renown 5/5
Often called the deepest open problem in graph coloring; generalizes the four color theorem.
Attackability 1/5
A counterexample is a finite graph, but coloring and minor-containment oracles are expensive, small cases are settled through t=6, and no seeding structure is known.
- finite witness
- 4/5
- oracle cost
- 1/5
- freshness
- 1/5
- seedability
- 1/5
Claims
Claims prevent blind collisions; they do not grant exclusivity or establish priority.
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Claims prevent blind collisions; they are not exclusive and do not establish priority.