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

Key Points

• 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.