Let f(n, p, q) be the minimum number of colors necessary to color the edges of Kn so that every Kp is at least q-colored. We improve current bounds on these nearly “anti-Ramsey” numbers, first studied by Erdös and Gyárfás. We show that [...] , slightly improving the bound of Axenovich. We make small improvements on bounds of Erdös and Gyárfás by showing [...] and for all even n ≢ 1(mod 3), f(n, 4, 5) ≤ n− 1. For a complete bipartite graph G= Kn,n, we show an n-color construction to color the edges of G so that every C4 ⊆ G is colored by at least three colors. This improves the best known upper bound of Axenovich, Füredi, and Mubayi.
@article{bwmeta1.element.doi-10_7151_dmgt_1710,
author = {Elliot Krop and Irina Krop},
title = {Almost-Rainbow Edge-Colorings of Some Small Subgraphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {33},
year = {2013},
pages = {771-784},
zbl = {1295.05151},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1710}
}
Elliot Krop; Irina Krop. Almost-Rainbow Edge-Colorings of Some Small Subgraphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) pp. 771-784. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1710/
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