Computing kernels in graphs with a clique-cutset
نویسندگان
چکیده
In a directed graph, a kernel is a subset of the vertices that is both independent and absorbing. Not all directed graphs have a kernel, and finding classes of graphs having always a kernel or for which deciding the existence of a kernel is polynomial has been the topic of many works in graph theory. We formalize some techniques to build a kernel in a graph with a clique-cutset, knowing kernels in the pieces with respect to the clique-cutset. As a consequence, we obtain for instance that computing a kernel in a clique-acyclic orientation of a chordal graph can be done in polynomial time. We enlighten some consequences in the theory of hedonic games.
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