A clique in a graph is a set of vertices, each of which is adjacent to every other vertex in this set. A k-clique relaxes this requirement, requiring vertices to be within a distance k of each other, rather than directly adjacent. In theory, a maximum clique algorithm can easily be adapted to solve the maximum k-clique problem. We use a state of the art maximum clique algorithm to show that this is feasible in practice, and introduce a lazy global domination rule which sometimes vastly reduces the search space. We include experimental results for a range of real-world and benchmark graphs, and a detailed look at random graphs.
@article{arxiv.1408.6485,
title = {Finding Maximum k-Cliques Faster using Lazy Global Domination},
author = {Ciaran McCreesh and Patrick Prosser},
journal= {arXiv preprint arXiv:1408.6485},
year = {2014}
}