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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 ...
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 ...
The Recursive Largest First (RLF) algorithm is a heuristic for the NP-hard graph coloring problem.It was originally proposed by Frank Leighton in 1979. [1]The RLF algorithm assigns colors to a graph’s vertices by constructing each color class one at a time.
Alice and Bob color the vertices of a graph G with a set k of colors. Alice and Bob take turns, coloring properly an uncolored vertex (in the standard version, Alice begins). If a vertex v is impossible to color properly (for any color, v has a neighbor colored with it), then Bob wins. If the graph is completely colored, then Alice wins.
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 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 ...
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.
Exact coloring of the complete graph K 6. Every n-vertex complete graph K n has an exact coloring with n colors, obtained by giving each vertex a distinct color. Every graph with an n-color exact coloring may be obtained as a detachment of a complete graph, a graph obtained from the complete graph by splitting each vertex into an independent set and reconnecting each edge incident to the ...