Geodesic
Rainbow numbers for small stars with one edge added
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 555-562

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A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. For a graph H and a positive integer n, the anti-Ramsey number f(n,H) is the maximum number of colors in an edge-coloring of Kₙ with no rainbow copy of H. The rainbow number rb(n,H) is the minimum number of colors such that any edge-coloring of Kₙ with rb(n,H) number of colors contains a rainbow copy of H. Certainly rb(n,H) = f(n,H) + 1. Anti-Ramsey numbers were introduced by Erdös et al. [5] and studied in numerous papers.
Keywords: rainbow number, anti-Ramsey number 
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Gorgol, Izolda; Łazuka, Ewa. Rainbow numbers for small stars with one edge added. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 4, pp. 555-562. http://geodesic.mathdoc.fr/item/DMGT_2010_30_4_a2/