combinatorics / Infinite combinatorics

Erdos Problems #593 and #1177

Erdos Problem #593 asks which finite triple systems occur in every uncountably chromatic triple system. The answer is exactly the class generated from private-vertex expansions of finite bipartite graphs by finite disjoint unions and one-point amalgamations. Problem #1177 on exact spectra is settled alongside it.

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combinatoricsJun 23, 2026Significance 13/100Registry: unreviewed

Erdos Problems #593 and #1177

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settles two numbered Erdos problems at once

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Erdos Problem #593 asks which finite triple systems occur in every uncountably chromatic triple system. The answer is exactly the class generated from private-vertex expansions of finite bipartite graphs by finite disjoint unions and one-point amalgamations. Problem #1177 on exact spectra is settled alongside it.

settles two numbered Erdos problems at once

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