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Chromatic boundedness for graphs with triangles excluding odd wheel t‑minors

Determine whether there exists a universal constant C such that every graph containing triangles and excluding odd wheels as t‑minors has chromatic number at most C.

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Background

The authors prove bounded chromatic number for triangle‑free graphs that exclude odd wheels as t‑minors and then note a gap: they do not know how to extend this boundedness to graphs that contain triangles while still excluding odd wheels as t‑minors. Clarifying chromatic behavior for this broader class would refine understanding of t‑minor‑based restrictions.

References

With more technical arguments we are able to prove that triangle-free graphs containing no odd wheel as a t-minor have bounded chromatic number, but we do not know how to do this for graphs containing triangles.

— Colouring t-perfect graphs (2412.17735 - Chudnovsky et al., 23 Dec 2024) in Section 3 (Reducing to the case where there are no short odd cycles), Remarks on Theorem 3.1