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Almost-Rainbow Edge-Colorings of Some Small Subgraphs

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Krop E., Krop I.

Discussiones Mathematicae Graph Theory

2013

tom 33

nr 4

771-784

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.

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1 Discussiones Mathematicae Graph Theory

1 Krop E.

1 Krop I.

1 2013

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Almost-Rainbow Edge-Colorings of Some Small Subgraphs