What question did this study set out to answer?

The aim is to establish the value of the star-critical weakened Gallai-Ramsey number gr_{\star}^{2,t}(C_5) for values of t.

April 3, 2026Open Access

The star-critical weakened Gallai-Ramsey number gr_^2, t (C₅)

Puntos clave

The aim is to establish the value of the star-critical weakened Gallai-Ramsey number gr_{\star}^{2,t}(C_5) for values of t.
Proving the equality gr_{\star}^{2,t}(C_5) = t for all t ≥ 3
Analyzing critical colorings of the graph C_5.
Demonstrating uniqueness of critical colorings up to isomorphism.
Confirmed that gr_{\star}^{2,t}(C_5) equals t for t greater than or equal to 3.
Proved that critical colorings of gr_{\star}^{2,t}(C_5) are unique except for color reordering.

Resumen

In this paper, we prove that the star-critical weakened Gallai-Ramsey number gr_^2, t (C₅) = t, for all t? 3. In the process, it is shown that the crtical coloring for gr_^2, t (C₅) is unique up to isomorphism or reordering of the colors.

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