Graph Coloring and Chromatic Number | GATECSE | Graph Theory

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graph coloring || chromatic number || chromatic number of the graph || vertex coloring || edge coloring || chromatic number in graph theory || coloring problem in graph theory || graph coloring in graph theory || vertex coloring in graph theory || chromatic number of a graph || chromatic number maximal clique theorem || chromatic number maximal clique || chromatic number of bipartite graph || chromatic number of complete graph

Graph coloring is a fundamental concept in graph theory where vertices are assigned colors so that no two adjacent vertices share the same color. The chromatic number is the smallest number required to color a graph without adjacent vertices having the same color. The process involves understanding the graph, selecting an appropriate algorithm, implementing it, finding the chromatic number, verifying the coloring, optimizing the algorithm, handling special cases, and testing the algorithm with different input graphs. Graph coloring and determining the chromatic number are NP-hard problems, but heuristic and exact algorithms can be used for special cases.

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