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Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅

100%

Urbański S.

Discussiones Mathematicae Graph Theory

1996

tom 16

nr 2

173-179

The paper gives an account of previous and recent attempts to determine the order of a smallest graph not containing K₅ and such that every 2-coloring of its edges results in a monochromatic triangle. A new 14-vertex K₄-free graph with the same Ramsey property in the vertex coloring case is found. This yields a new construction of one of the only two known 15-vertex (3,3)-Ramsey graphs not containing K₅.

Almost-Rainbow Edge-Colorings of Some Small Subgraphs

88%

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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2 Discussiones Mathematicae Graph Theory

1 Krop E.

1 Krop I.

1 Urbański S.

1 2013

1 1996

Wyniki wyszukiwania

Remarks on 15-vertex (3,3)-ramsey graphs not containing K₅

Almost-Rainbow Edge-Colorings of Some Small Subgraphs