Research notes on every problem, and a library of the papers behind them. Built from the open erdos repository.

Updated Oct 7

Problem 738

Statement. If $G$ has infinite chromatic number and is triangle-free (contains no $K_3$ ) then must $G$ contain every tree as an induced subgraph?

Status. Open.

Source. erdosproblems.com/738, accessed 2026-09-04. Cite as: T. F. Bloom, Erdős Problem #738, https://www.erdosproblems.com/738.

Formalization. None recorded.

Progress

Not yet compiled.

Known Results

Not yet compiled.

Linked library material

These entries are derived from explicit links on library pages. They are navigation only and do not by themselves record mathematical progress.

Linked from (7)

Graph Coloring graph_coloring/scott_2018_survey_chi_boundedness 3.1 (p. 4): the Gyárfás–Sumner conjecture, all forests are χ-bounding 3.3 (p. 4): for every tree T, graphs with no induced subdivision of T are χ-bounded 3.4 (p. 5): every path is χ-bounding 3.5 (p. 6): trees from a radius-two tree by subdividing once some root edges are χ-bounding 3.6 (pp. 6–7): three families of trees with two far-apart branch vertices are χ-bounding

Graph