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. We show that in all nontrivial cases.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1513,
author = {Izolda Gorgol and Ewa \L azuka},
title = {Rainbow numbers for small stars with one edge added},
journal = {Discussiones Mathematicae Graph Theory},
volume = {30},
year = {2010},
pages = {555-562},
zbl = {1217.05161},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1513}
}
Izolda Gorgol; Ewa Łazuka. Rainbow numbers for small stars with one edge added. Discussiones Mathematicae Graph Theory, Tome 30 (2010) pp. 555-562. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1513/
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