Skip to content

Add Erdős Problem 603 (chromatic Property B for intersection ≠ 2)#3776

Open
henrykmichalewski wants to merge 2 commits intogoogle-deepmind:mainfrom
henrykmichalewski:add-problem-603
Open

Add Erdős Problem 603 (chromatic Property B for intersection ≠ 2)#3776
henrykmichalewski wants to merge 2 commits intogoogle-deepmind:mainfrom
henrykmichalewski:add-problem-603

Conversation

@henrykmichalewski
Copy link
Copy Markdown
Member

@henrykmichalewski henrykmichalewski commented Apr 16, 2026

fixes #822

Problem

Erdős Problem 603: https://www.erdosproblems.com/603 (sister problem of 602)

Does every family of sets, any two of which intersect in at most 2 points, have chromatic Property B?

Contents

  • HasChromaticPropertyB definition generalizing Problem 602
  • Main open theorem erdos_603
  • Komjáth's ≠1 intersection result as context
  • 4 proved variants (finite family, singleton family, pairwise disjoint, large sets)
  • Disproof of a misformalization (showing the naive encoding is too weak)
  • Sanity checks ensuring definitions are non-trivial

Assisted by Claude (Anthropic).

…ion ≠ 2

Adds formalization of Erdős Problem 603 (sister problem of 602).
Reference: https://www.erdosproblems.com/603

Asks whether every family of sets, any two of which intersect in at most
2 points, has chromatic Property B. Includes HasChromaticPropertyB
definition generalizing 602, Komjáth's ≠1 result as context, 4 proved
variants, disproof of a misformalization, and sanity checks. Assisted by
Claude (Anthropic).
@github-actions github-actions Bot added the erdos-problems Erdős Problems label Apr 16, 2026
@henrykmichalewski
Copy link
Copy Markdown
Member Author

Closes #822

Mirrors the Round C docstring pass from the private repo's
phase1-infrastructure branch. Each Lean file now carries the
canonical source statement and upstream URL inline so reviewers
can verify formalization against the source without navigating
away from the diff.
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

erdos-problems Erdős Problems

Projects

None yet

Development

Successfully merging this pull request may close these issues.

Erdős Problem 603

1 participant