## Abstract

Let C be a proper minor-closed family of graphs. We present a randomized algorithm that given a graph G∈C with n vertices, finds a simple cycle of size k in G (if exists) in 2^{O(k)}n time. The algorithm applies to both directed and undirected graphs. In previous linear time algorithms for this problem, the runtime dependence on k is super-exponential. The algorithm can be derandomized yielding a 2^{O(k)}nlogn time algorithm.

Original language | American English |
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Pages (from-to) | 74-85 |

Number of pages | 12 |

Journal | Theoretical Computer Science |

Volume | 842 |

DOIs | |

State | Published - 24 Nov 2020 |

## Keywords

- Linear time algorithm
- Minor-closed graph family
- Parameterized algorithm
- k-cycle

## All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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