A Self-Stabilizing (Δ+4)-Edge-Coloring Algorithm for Planar Graphs in Anonymous Uniform Systems

A Fault-Containing Self-Stabilizing Algorithm for 6-Coloring Planar Graphs

This paper presents the first fault-containing self-stabilizing algorithm which can 6color any planar graph. Besides the capability to contain the fault in any single-fault situation, the proposed algorithm also has the capability to stabilize faster in single-fault situations. For single-fault situations, the worst-case stabilization time of the proposed algorithm is O(Δ), whereas the worst-ca...

Observations on Self - Stabilizing Graph

We investigate the existence of deterministic uniform self-stabilizing algorithms (DUSSAs) for a number or problems on connected undirected graphs. This investigation is carried out under three models of parallelism, namely central daemon, restricted parallelism, and maximal paral-lelism. We observe that for several problems including 2-coloring odd-degree complete bipartite graphs, 2-coloring ...

A self-stabilizing distributed algorithm for edge-coloring general graphs

Acyclic edge coloring of planar graphs with Δ colors

An acyclic edge coloring of a graph is a proper edge coloring without bichromatic cycles. In 1978, it was conjectured that ∆(G) + 2 colors suffice for an acyclic edge coloring of every graph G [6]. The conjecture has been verified for several classes of graphs, however, the best known upper bound for as special class as planar graphs are, is ∆+12 [2]. In this paper, we study simple planar graph...

A practical algorithm for [r, s, t]-coloring of graph

Coloring graphs is one of important and frequently used topics in diverse sciences. In the majority of the articles, it is intended to find a proper bound for vertex coloring, edge coloring or total coloring in the graph. Although it is important to find a proper algorithm for graph coloring, it is hard and time-consuming too. In this paper, a new algorithm for vertex coloring, edge coloring an...