Almost-Rainbow Edge-Colorings of Some Small Subgraphs
Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 4, p. 771.

Voir la notice de l'article dans European Digital Mathematics Library

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.
Classification : 05C15, 05C38, 05C55
Mots-clés : Ramsey theory, generalized Ramsey theory, rainbow-coloring, edge-coloring, Erdös problem, Erdős problem
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     author = {Elliot Krop and Irina Krop},
     title = {Almost-Rainbow {Edge-Colorings} of {Some} {Small} {Subgraphs}},
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Elliot Krop; Irina Krop. Almost-Rainbow Edge-Colorings of Some Small Subgraphs. Discussiones Mathematicae Graph Theory, Tome 33 (2013) no. 4, p. 771. https://geodesic-test.mathdoc.fr/item/DMGT_2013__33_4_268325/