Coloration de nombre de Grundy pour les graphes triangul\'es

TL;DR

This paper explores the Grundy coloring number for triangulated graphs and discusses its applications in dynamic network routing and frequency assignment, emphasizing the need for adaptable coloring strategies in unstable, changing networks.

Contribution

It introduces a new approach to Grundy coloring in triangulated graphs with applications to dynamic network routing and frequency allocation.

Findings

Proposes a coloring method for stable frequency assignment.

Addresses dynamic topology changes in ad hoc networks.

Highlights the importance of adaptable coloring algorithms.

Abstract

The problem of the data routing management, it provides a method or a strategy that guarantees at any time the connection between any pair of nodes in the network. This routing method must be able to cope with frequent changes in the topology and also other characteristics of the ad hoc network as bandwidth, the number of links, network resources etc.. We also illustrate the utility of the proposed algorithms: the problem of assignment or frequency allotment in a radio network or mobile phones as in the following way: how to attribute a frequency to every transmitter(issuer) or an unity(unit) of the network, so that two broadcasting stations (issuers) which can interfere have frequencies distant enough from each other ? Thus to affect the wavelengths means finding a coloring of the graph, but because the network is not stable and the topology is dynamic, we need a method which maintains the initial allocation of the frequencies or to look for a new allocation to maintain the stability of the network.