Displaying similar documents to “Rainbow Ramsey theorems for colorings establishing negative partition relations”

Rainbow Ramsey theory.

Jungić, Veselin, Nešetřil, Jaroslav, Radoičić, Radoš (2005)

Integers

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Three edge-coloring conjectures

Richard H. Schelp (2002)

Discussiones Mathematicae Graph Theory

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The focus of this article is on three of the author's open conjectures. The article itself surveys results relating to the conjectures and shows where the conjectures are known to hold.

Bounds for the b-Chromatic Number of Subgraphs and Edge-Deleted Subgraphs

P. Francis, S. Francis Raj (2016)

Discussiones Mathematicae Graph Theory

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A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we obtain bounds for the b- chromatic number of induced subgraphs in terms of the b-chromatic number of the original graph. This turns out to be...

On acyclic colorings of direct products

Simon Špacapan, Aleksandra Tepeh Horvat (2008)

Discussiones Mathematicae Graph Theory

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A coloring of a graph G is an acyclic coloring if the union of any two color classes induces a forest. It is proved that the acyclic chromatic number of direct product of two trees T₁ and T₂ equals min{Δ(T₁) + 1, Δ(T₂) + 1}. We also prove that the acyclic chromatic number of direct product of two complete graphs Kₘ and Kₙ is mn-m-2, where m ≥ n ≥ 4. Several bounds for the acyclic chromatic number of direct products are given and in connection to this some questions are raised. ...