Displaying similar documents to “Optimal on-line coloring of circular arc graphs”

On-line 𝓟-coloring of graphs

Piotr Borowiecki (2006)

Discussiones Mathematicae Graph Theory

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For a given induced hereditary property 𝓟, a 𝓟-coloring of a graph G is an assignment of one color to each vertex such that the subgraphs induced by each of the color classes have property 𝓟. We consider the effectiveness of on-line 𝓟-coloring algorithms and give the generalizations and extensions of selected results known for on-line proper coloring algorithms. We prove a linear lower bound for the performance guarantee function of any stingy on-line 𝓟-coloring algorithm. In the...

Graph Radiocoloring Concepts

R. Kalfakakou, G. Nikolakopoulou, E. Savvidou, M. Tsouros (2003)

The Yugoslav Journal of Operations Research

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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.

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,...

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...