Displaying similar documents to “Sum list coloring 2 × n arrays.”

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...

Rainbow Ramsey theorems for colorings establishing negative partition relations

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.

The Incidence Chromatic Number of Toroidal Grids

Éric Sopena, Jiaojiao Wu (2013)

Discussiones Mathematicae Graph Theory

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An incidence in a graph G is a pair (v, e) with v ∈ V (G) and e ∈ E(G), such that v and e are incident. Two incidences (v, e) and (w, f) are adjacent if v = w, or e = f, or the edge vw equals e or f. The incidence chromatic number of G is the smallest k for which there exists a mapping from the set of incidences of G to a set of k colors that assigns distinct colors to adjacent incidences. In this paper, we prove that the incidence chromatic number of the toroidal grid Tm,n = Cm2Cn equals...

Rainbow Ramsey theory.

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

Integers

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Neochromatica

Panagiotis Cheilaris, Ernst Specker, Stathis Zachos (2010)

Commentationes Mathematicae Universitatis Carolinae

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We create and discuss several modifications to traditional graph coloring. In particular, we classify various notions of coloring in a proper hierarchy. We concentrate on grid graphs whose colorings can be represented by natural number entries in arrays with various restrictions.

Coloring with no 2-colored P 4 's.

Albertson, Michael O., Chappell, Glenn G., Kierstead, H.A., Kündgen, André, Ramamurthi, Radhika (2004)

The Electronic Journal of Combinatorics [electronic only]

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