The degeneracy of an n-vertex graph G is the smallest number k such that every subgraph of G contains a vertex of degree at most k. We present an algorithm for enumerating all simple cycles of length p in an n-order k-degenerate graph running in time O(n⌊p/2⌋ k⌈p/2⌉). We then show that this algorithm is worst-case output size optimal by proving a Θ(n⌊p/2⌋ k⌈p/2⌉) bound on the maximal number of simple p-length cycles in these graphs. Our results also apply to induced (chordless) cycles.
CITATION STYLE
Manoussakis, G. (2017). Listing all fixed-length simple cycles in sparse graphs in optimal time. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10472 LNCS, pp. 355–366). Springer Verlag. https://doi.org/10.1007/978-3-662-55751-8_28
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