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In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring [1] is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but ...
In graph theory, graph coloring is a special case of graph labeling; ... the greedy coloring algorithm can be used to find optimal colorings in polynomial time, ...
The numbers indicate the order in which the greedy algorithm colors the vertices. In graph theory, the Grundy number or Grundy chromatic number of an undirected graph is the maximum number of colors that can be used by a greedy coloring strategy that considers the vertices of the graph in sequence and assigns each vertex its first available ...
If the graph has a vertex v with degree less than Δ, then a greedy coloring algorithm that colors vertices farther from v before closer ones uses at most Δ colors. This is because at the time that each vertex other than v is colored, at least one of its neighbors (the one on a shortest path to v ) is uncolored, so it has fewer than Δ colored ...
The greedy coloring algorithm, when applied to a given ordering of the vertices of a graph G, considers the vertices of the graph in sequence and assigns each vertex its first available color, the minimum excluded value for the set of colors used by its neighbors. Different vertex orderings may lead this algorithm to use different numbers of ...
Greedy algorithms determine the minimum number of coins to give while making change. These are the steps most people would take to emulate a greedy algorithm to represent 36 cents using only coins with values {1, 5, 10, 20}. The coin of the highest value, less than the remaining change owed, is the local optimum.
Crown graphs can be used to show that greedy coloring algorithms behave badly in the worst case: if the vertices of a crown graph are presented to the algorithm in the order u 0, v 0, u 1, v 1, etc., then a greedy coloring uses n colors, whereas the optimal number of colors is two.
The graph of an octahedron is complete multipartite (K 2,2,2) and well-colored.. In graph theory, a subfield of mathematics, a well-colored graph is an undirected graph for which greedy coloring uses the same number of colors regardless of the order in which colors are chosen for its vertices.