Displaying similar documents to “On the cost chromatic number of outerplanar, planar, and line graphs”

K3-Worm Colorings of Graphs: Lower Chromatic Number and Gaps in the Chromatic Spectrum

Csilla Bujtás, Zsolt Tuza (2016)

Discussiones Mathematicae Graph Theory

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A K3-WORM coloring of a graph G is an assignment of colors to the vertices in such a way that the vertices of each K3-subgraph of G get precisely two colors. We study graphs G which admit at least one such coloring. We disprove a conjecture of Goddard et al. [Congr. Numer. 219 (2014) 161-173] by proving that for every integer k ≥ 3 there exists a K3-WORM-colorable graph in which the minimum number of colors is exactly k. There also exist K3-WORM colorable graphs which have a K3-WORM...

Ramseyan properties of graphs.

DeLaVina, Ermelinda, Fajtlowicz, Siemion (1996)

The Electronic Journal of Combinatorics [electronic only]

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Optimal Backbone Coloring of Split Graphs with Matching Backbones

Krzysztof Turowski (2015)

Discussiones Mathematicae Graph Theory

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For a graph G with a given subgraph H, the backbone coloring is defined as the mapping c : V (G) → N+ such that |c(u) − c(v)| ≥ 2 for each edge {u, v} ∈ E(H) and |c(u) − c(v)| ≥ 1 for each edge {u, v} ∈ E(G). The backbone chromatic number BBC(G,H) is the smallest integer k such that there exists a backbone coloring with maxv∈V (G) c(v) = k. In this paper, we present the algorithm for the backbone coloring of split graphs with matching backbone.

Generalized total colorings of graphs

Mieczysław Borowiecki, Arnfried Kemnitz, Massimiliano Marangio, Peter Mihók (2011)

Discussiones Mathematicae Graph Theory

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An additive hereditary property of graphs is a class of simple graphs which is closed under unions, subgraphs and isomorphism. Let P and Q be additive hereditary properties of graphs. A (P,Q)-total coloring of a simple graph G is a coloring of the vertices V(G) and edges E(G) of G such that for each color i the vertices colored by i induce a subgraph of property P, the edges colored by i induce a subgraph of property Q and incident vertices and edges obtain different colors. In this...

List coloring of complete multipartite graphs

Tomáš Vetrík (2012)

Discussiones Mathematicae Graph Theory

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The choice number of a graph G is the smallest integer k such that for every assignment of a list L(v) of k colors to each vertex v of G, there is a proper coloring of G that assigns to each vertex v a color from L(v). We present upper and lower bounds on the choice number of complete multipartite graphs with partite classes of equal sizes and complete r-partite graphs with r-1 partite classes of order two.

k -Ramsey classes and dimensions of graphs

Jan Kratochvíl (1995)

Commentationes Mathematicae Universitatis Carolinae

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In this note, we introduce the notion of k -Ramsey classes of graphs and we reveal connections to intersection dimensions of graphs.

The chromaticity of a family of 2-connected 3-chromatic graphs with five triangles and cyclomatic number six

Halina Bielak (1998)

Discussiones Mathematicae Graph Theory

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In this note, all chromatic equivalence classes for 2-connected 3-chromatic graphs with five triangles and cyclomatic number six are described. New families of chromatically unique graphs of order n are presented for each n ≥ 8. This is a generalization of a result stated in [5]. Moreover, a proof for the conjecture posed in [5] is given.

Grundy number of graphs

Brice Effantin, Hamamache Kheddouci (2007)

Discussiones Mathematicae Graph Theory

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The Grundy number of a graph G is the maximum number k of colors used to color the vertices of G such that the coloring is proper and every vertex x colored with color i, 1 ≤ i ≤ k, is adjacent to (i-1) vertices colored with each color j, 1 ≤ j ≤ i -1. In this paper we give bounds for the Grundy number of some graphs and cartesian products of graphs. In particular, we determine an exact value of this parameter for n-dimensional meshes and some n-dimensional toroidal meshes. Finally,...

Equitable Colorings Of Corona Multiproducts Of Graphs

Hanna Furmánczyk, Marek Kubale, Vahan V. Mkrtchyan (2017)

Discussiones Mathematicae Graph Theory

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A graph is equitably k-colorable if its vertices can be partitioned into k independent sets in such a way that the numbers of vertices in any two sets differ by at most one. The smallest k for which such a coloring exists is known as the equitable chromatic number of G and denoted by 𝜒=(G). It is known that the problem of computation of 𝜒=(G) is NP-hard in general and remains so for corona graphs. In this paper we consider the same model of coloring in the case of corona multiproducts...

2-distance 4-colorability of planar subcubic graphs with girth at least 22

Oleg V. Borodin, Anna O. Ivanova (2012)

Discussiones Mathematicae Graph Theory

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The trivial lower bound for the 2-distance chromatic number χ₂(G) of any graph G with maximum degree Δ is Δ+1. It is known that χ₂ = Δ+1 if the girth g of G is at least 7 and Δ is large enough. There are graphs with arbitrarily large Δ and g ≤ 6 having χ₂(G) ≥ Δ+2. We prove the 2-distance 4-colorability of planar subcubic graphs with g ≥ 22.