K Coloring Np Complete

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16 Mar, 2022

NP-Completeness Graph Coloring Graph K-coloring Problem. A K-coloring problem for undirected graphs is an assignment of colors to the nodes of the graph such that no two adjacent vertices have the same color and at most K colors are used to complete color the graph.

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NP-hardness is a precise concept.

K coloring np complete. Begingroup I take issue with the sentence Therefore if P1 is solved we know solution to P2. Likewise the question Is a triangle-free graph k-colorable is shown to be NP-complete for any fixed value of k. Remains NP-complete when restricted to the class of triangle-free graphs with maximum degree 4.

Given a graph GV E and an integer K.

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