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WordNet-Online
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Definitions from the WebTerm: Coloring the GraphDescription:Coloring the graph refers to the process of assigning colors to the vertices of a graph, following certain rules or conditions. This technique is commonly used in graph theory, computer science, and mathematics to study different properties and relationships within a graph. Senses:1. Coloring the Graph (Graph Theory):In the context of graph theory, coloring the graph involves assigning colors to the vertices of a graph, subject to specific conditions or constraints. The goal is to ensure that no adjacent vertices share the same color. Example Sentence:In order to prove the four-color theorem, mathematicians had to meticulously work on coloring the graph without any adjacent vertices having the same color. 2. Coloring the Graph (Computer Science):In computer science, coloring the graph is a fundamental concept used in many applications, such as scheduling, map coloring, and register allocation. It involves assigning colors or labels to nodes or elements in a graph to signify different attributes, dependencies, or states. Example Sentence:When optimizing the allocation of registers, the compiler uses various techniques, including coloring the graph based on the registers availability and dependencies. 3. Coloring the Graph (Mathematics):In mathematics, coloring the graph is often employed to determine the minimum number of colors required to color a graph without adjacent vertices sharing the same color. This area of study is closely related to graph coloring problems and the concept of chromatic number. Example Sentence:Researchers were able to prove the conjecture by finding the chromatic number for the given graph, which required coloring the graph using the minimum number of colors. Related Products: | ||||
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