A linear algorithm for coloring vertices of a graph or finding a Meyniel obstruction
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چکیده
A Meyniel obstruction is an odd cycle with at most one chord and a graph is Meyniel if and only if it has no Meyniel obstruction. The authors have found in a previous work a linear-time algorithm for optimaly color the vertices of a Meyniel graph. Here we extend this algorithm to obtain a linear-time algorithm that, for any graph, colors optimally the vertices of the graph or finds a Meyniel obstruction.
منابع مشابه
Coloring vertices of a graph or finding a Meyniel obstruction
A Meyniel obstruction is an odd cycle with at least five vertices and at most one chord. A graph is Meyniel if and only if it has no Meyniel obstruction as an induced subgraph. Here we give a O(n) algorithm that, for any graph, finds either a clique and coloring of the same size or a Meyniel obstruction. We also give a O(n) algorithm that, for any graph, finds either an easily recognizable stro...
متن کاملColoring Meyniel graphs in linear time
A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. We present a linear-time algorithm that colors optimally the vertices of a Meyniel graph and finds a clique of maximum size.
متن کاملالگوریتم ژنتیک با جهش آشوبی هوشمند و ترکیب چند‌نقطه‌ای مکاشفه‌ای برای حل مسئله رنگ‌آمیزی گراف
Graph coloring is a way of coloring the vertices of a graph such that no two adjacent vertices have the same color. Graph coloring problem (GCP) is about finding the smallest number of colors needed to color a given graph. The smallest number of colors needed to color a graph G, is called its chromatic number. GCP is a well-known NP-hard problems and, therefore, heuristic algorithms are usually...
متن کاملErratum : MCColor is not optimal on Meyniel graphs
A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. In [2] we claimed that our algorithm MCColor produces an optimal coloring for every Meyniel graph. But later we found a mistake in the proof and a couterexample to the optimality, which we present here. MCColor can still be used to find a stable set that intersects all maximal cliques of a Meyniel graph ...
متن کاملA 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...
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تاریخ انتشار 2005