2022
DOI: 10.48550/arxiv.2202.04476
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Counting Kernels in Directed Graphs with Arbitrary Orientations

Abstract: A kernel of a directed graph is a subset of vertices that is both independent and absorbing (every vertex not in the kernel has an out-neighbour in the kernel).Not all directed graphs contain kernels, and computing a kernel or deciding that none exist is NP-complete even on low-degree planar digraphs. The existing polynomial-time algorithms for this problem all restrict both the undirected structure and the edge orientations of the input: for example, to chordal graphs without bidirectional edges (Pass-Lanneau… Show more

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