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Every graph with no K_t minor is (t-1)-colorable.

Status is community- and machine-tracked and may lag. Verify independently before investing effort.

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

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Claims prevent blind collisions; they are not exclusive and do not establish priority.