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Graph coloring enjoys many practical applications as well as theoretical challenges. Beside the classical types of problems, different limitations can also be set on the graph, or on the way a color is assigned, or even on the color itself. It has even reached popularity with the general public in the form of the popular number puzzle Sudoku ...
The RLF algorithm assigns colors to a graph’s vertices by constructing each color class one at a time. It does this by identifying a maximal independent set of vertices in the graph, assigning these to the same color, and then removing these vertices from the graph. These actions are repeated on the remaining subgraph until no vertices remain.
In computer science and graph theory, the term color-coding refers to an algorithmic technique which is useful in the discovery of network motifs. For example, it can be used to detect a simple path of length k in a given graph. The traditional color-coding algorithm is probabilistic, but it can be derandomized without much overhead in the ...
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 ...
By applying exact algorithms for vertex coloring to the line graph of the input graph, it is possible to optimally edge-color any graph with m edges, regardless of the number of colors needed, in time 2 m m O(1) and exponential space, or in time O(2.2461 m) and only polynomial space (Björklund, Husfeldt & Koivisto 2009).
In graph theory and theoretical computer science, the colour refinement algorithm also known as the naive vertex classification, or the 1-dimensional version of the Weisfeiler-Leman algorithm, is a routine used for testing whether two graphs are isomorphic. [1]
Domain coloring plot of the function f(x) = (x 2 − 1)(x − 2 − i) 2 / x 2 + 2 + 2i , using the structured color function described below.. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane.
Given a graph G and given a set L(v) of colors for each vertex v (called a list), a list coloring is a choice function that maps every vertex v to a color in the list L(v).As with graph coloring, a list coloring is generally assumed to be proper, meaning no two adjacent vertices receive the same color.