Further results on the achromatic number
Dennis Geller, Hudson Kronk (1974)
Fundamenta Mathematicae
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Dennis Geller, Hudson Kronk (1974)
Fundamenta Mathematicae
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András Hajnal (2008)
Fundamenta Mathematicae
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Given a function f, a subset of its domain is a rainbow subset for f if f is one-to-one on it. We start with an old Erdős problem: Assume f is a coloring of the pairs of ω₁ with three colors such that every subset A of ω₁ of size ω₁ contains a pair of each color. Does there exist a rainbow triangle? We investigate rainbow problems and results of this style for colorings of pairs establishing negative "square bracket" relations.
Ding, Man, Sun, Wei, Chen, Hanning (2010)
Mathematical Problems in Engineering
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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.
Exoo, Geoffrey (1998)
The Electronic Journal of Combinatorics [electronic only]
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Philippe Meurdesoif, Benoît Rottembourg (2001)
RAIRO - Operations Research - Recherche Opérationnelle
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In this paper we will describe a new class of coloring problems, arising from military frequency assignment, where we want to minimize the number of distinct -uples of colors used to color a given set of -complete-subgraphs of a graph. We will propose two relaxations based on Semi-Definite Programming models for graph and hypergraph coloring, to approximate those (generally) NP-hard problems, as well as a generalization of the works of Karger et al. for hypergraph coloring, to find...
Jungić, Veselin, Nešetřil, Jaroslav, Radoičić, Radoš (2005)
Integers
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Sabo, Dusty, Schaal, Daniel, Tokaz, Jacent (2007)
Integers
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Jungić, Veselin, Radoičić, Radoš (2003)
Integers
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Jasmina Fijuljanin (2012)
The Yugoslav Journal of Operations Research
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Axenovich, Maria, Manske, Jacob (2008)
Integers
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Isaak, Garth (2002)
The Electronic Journal of Combinatorics [electronic only]
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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...
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. ...