Grundy Packing Coloring of Graphs
Didem G\"oz\"upek, Iztok Peterin

TL;DR
This paper introduces the Grundy packing chromatic number, a new graph invariant related to packing colorings, and provides algorithms, properties, bounds, and complexity results for it.
Contribution
It defines the Grundy packing chromatic number, presents a polynomial-time greedy algorithm, and explores its properties and computational complexity.
Findings
Polynomial-time greedy algorithm for packing coloring
Bounds and exact results for Grundy packing chromatic number
Complexity analysis of the problem
Abstract
A map of a graph is a packing -coloring if every two different vertices of the same color are at distance more than . The packing chromatic number of is the smallest integer such that there exists a packing -coloring. In this paper we introduce the notion of \textit{Grundy packing chromatic number}, analogous to the Grundy chromatic number of a graph. We first present a polynomial-time algorithm that is based on a greedy approach and gives a packing coloring of . We then define the Grundy packing chromatic number of a graph as the maximum value that this algorithm yields in a graph . We present several properties of , provide results on the complexity of the problem as well as bounds and some exact results for .
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Taxonomy
Topicsgraph theory and CDMA systems · Graph Labeling and Dimension Problems · Advanced Graph Theory Research
