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What NP-complete problem to reduce to k-Edge-Colorability to prove its NP-hardness?

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Problem Detail: 

What known NP-complete problem would one reduce to $k$-Edge-Colorability to prove that the latter is NP-hard?

Asked By : Omid Ebrahimi
Answered By : Juho

This is a classic result of Holyer [1]. The reduction is from 3-SAT, and the constructed graph is cubic.

[1] Holyer, Ian. "The NP-completeness of edge-coloring." SIAM Journal on Computing 10.4 (1981): 718-720.

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