Add Max-k-cut application

[clausia]

What is the expected behavior?

Being able to solve a Max-k-cut type problem

In the Max-k-Cut problem, we are given an undirected graph, G=(V, E), with non-negative edge weights. Our objective is to divide the vertices into at most k disjoint sets, for some given positive integer k, to maximize the weight of the edges whose endpoints lie in different sets. When k=2, this problem is known simply as the Max-Cut problem.

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Add Max-k-cut application

We propose to add the functionality to be able to solve the Max-k-cut problem, similar to how the class that contains the Maxcut application already exists.

We have already made progress on this project between Vyron Vasileiadis (@fedonman) and myself (Claudia Zendejas-Morales, @clausia), we raise it in this issue to be able to discuss any concerns that may arise in this regard.

Furthermore, we have analyzed the solution for Maxcut that exists here in this qiskit-optimization project, as well as the solution proposed in work [1].

Please let us know any comments you have on this proposal.

[1] Zsolt Tabi; Kareem H. El-Safty; Zsófia Kallus; Péter Hága; Tamás Kozsik; Adam Glos; Zoltán Zimborás Quantum Optimization for the Graph Coloring Problem with Space-Efficient Embedding https://ieeexplore.ieee.org/document/9259934