- Indeed, for sparse graphs, the standard greedy coloring strategy of choosing the first available color achieves this competitive ratio, and it is possible to prove a matching lower bound on the competitive ratio of any online coloring algorithm.
- In comparison to earlier algorithms described in the published article the MaxCliqueDyn algorithm is improved by an improved approximate coloring algorithm ( ColorSort algorithm ) and by applying tighter, more computationally expensive upper bounds on a fraction of the search space.
- A greedy coloring algorithm that considers the edges of a graph or multigraph one by one, assigning each edge the first available color, may sometimes use as many as colors, which may be nearly twice as many number of colors as is necessary.
- For chordal graphs, and for special cases of chordal graphs such as interval graphs and indifference graphs, the greedy coloring algorithm can be used to find optimal colorings in polynomial time, by choosing the vertex ordering to be the reverse of a perfect elimination ordering for the graph.
- The same property is true for a larger class of graphs, the distance-hereditary graphs : distance-hereditary graphs are perfectly orderable, with a perfect ordering given by the reverse of a lexicographic ordering, so lexicographic breadth-first search can be used in conjunction with greedy coloring algorithms to color them optimally in linear time.
- It's difficult to find coloring algorithm in a sentence. 用coloring algorithm造句挺難的
- 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.
- Every graph " G " has a vertex with at most O ( " h " ( " G " ) ) incident edges, from which it follows that a greedy coloring algorithm that removes this low-degree vertex, colors the remaining graph, and then adds back the removed vertex and colors it, will color the given graph with O ( " h " ( " G " ) ) colors.