The board / graph theory / #1068
Erdős Problem #1068
OPENdatabase updated 2025-10-01
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Does every graph with chromatic number \(\aleph_1\) contain a countable subgraph which is infinitely connected?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/1068.Prizenone
Topicsgraph theory, set theory, chromatic number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1068
Attempts
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The two page-cited ZFC constructions are verified to contain \(K_{\aleph_0}\); an ordered lower-clique theorem and exact truncation formulas are proved, while the general problem remains open at the c
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