NP completeness of finding the chromatic index of regular graphs

doi:10.1016/0196-6774(83)90032-9

Journal of Algorithms

Volume 4, Issue 1, March 1983, Pages 35-44

https://doi.org/10.1016/0196-6774(83)90032-9 Get rights and content

Abstract

We show that it is NP complete to determine whether it is possible to edge color a regular graph of degree k with k colors for any k ⩾ 3. As a by-product of this result, we obtain a new way to generate k-regular graphs which are k-edge colorable.

References (5)

H Izbicki
An edge coloring problem
I.J Holyer
The Computational Complexity of Graph Theory Problems

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In this paper, we exhibit an irreducible Markov chain $M$ on the edge $k$ -colorings of bipartite graphs based on certain properties of the solution space. We show that diameter of this Markov chain grows linearly with the number of edges in the graph and with the number of colors. We also prove a polynomial upper bound on the inverse of acceptance ratio of the Metropolis–Hastings algorithm when the algorithm is applied on $M$ with the uniform distribution of all possible edge $k$ -colorings of $G$ . A special case of our results is the solution space of the possible completions of Latin rectangles.
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NP completeness of finding the chromatic index of regular graphs

Abstract

An edge coloring problem

The Computational Complexity of Graph Theory Problems