Erdős problem 593 · problems.science

Which finite triple systems occur in every triple system of uncountable chromatic number? The claimed characterization: exactly those that, after removing isolated vertices, are linear, have every hyperedge-node of their Levi graph meeting a bridge, and have every Berge cycle even.

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12 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

593.lean

Retained formal statement2 of 10

The empty hypergraph is trivially obligatory: The 3-uniform hypergraph on PEmpty (no vertices, no edges) appears in every hypergraph via the empty injection.

This degenerate case confirms the definition is well-formed.

FormalConjectures/ErdosProblems/593.leanErdos593.erdos_593.variants.empty_hypergraph_obligatory1 lineExact file

1IsObligatory { edges := ∅, uniform := ⋯ }

TextbookStatement only, no proof

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