From 3-Coloring to Edge Coloring
Pedagogical Contributions for Learning in the Scope of Computation Theory
DOI:
https://doi.org/10.20873/uft.2675-3588.2026.v7n2.p81-90Keywords:
NP-Completeness, Edge Coloring, Vertex Coloring, Polynomial Reductions, Computational ComplexityAbstract
This article examines the NP-completeness of the Edge Coloring problem through a polynomial reduction chain starting from the 3-Coloring problem. The methodology employs a Line Graph to demonstrate membership in NP and establishes NP-Hardness via reductions from 3-SAT, following Holyer's construction. We present formal definitions, historical context, and a review of fundamental works in computational complexity theory. The main result demonstrates that Edge Coloring is NP-complete using a clear and accessible reduction method. The work provides educational examples with visual illustrations and step-by-step explanations of logical gadgets. This material serves as a learning resource to help students understand polynomial reductions and NP-completeness concepts in computer science courses.
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Copyright (c) 2026 Ana Júlia Campos Vieira, Dallyla de Moraes Sousa, Daniel Martins da Silva, Tanilson Dias dos Santos
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