Displaying similar documents to “On growth rates of permutations, set partitions, ordered graphs and other objects.”

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...

Coloring Some Finite Sets in ℝn

József Balogh, Alexandr Kostochka, Andrei Raigorodskii (2013)

Discussiones Mathematicae Graph Theory

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This note relates to bounds on the chromatic number χ(ℝn) of the Euclidean space, which is the minimum number of colors needed to color all the points in ℝn so that any two points at the distance 1 receive different colors. In [6] a sequence of graphs Gn in ℝn was introduced showing that . For many years, this bound has been remaining the best known bound for the chromatic numbers of some lowdimensional spaces. Here we prove that and find an exact formula for the chromatic number in...

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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