## Abstract

The degeneracy of a graph G is the smallest integer k such that every subgraph of G contains a vertex of degree at most k. Given an n-order k-degenerate graph G, we present an algorithm for enumerating all its maximal cliques. Assuming that α is the number of maximal cliques of G, our algorithm has setup time O(n(k^{2} +s(k +1))) and enumeration time αO((k + 1)f(k + 1)) where s(k + 1) (resp. f(k + 1)) is the preprocessing time (resp. enumeration time) for maximal clique enumeration in a general (k + 1)-order graph. This is the first output sensitive algorithm whose enumeration time depends only on the degeneracy of the graph.

Original language | English |
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Title of host publication | 12th International Symposium on Parameterized and Exact Computation, IPEC 2017 |

Editors | Daniel Lokshtanov, Naomi Nishimura |

Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

ISBN (Electronic) | 9783959770514 |

DOIs | |

State | Published - 1 Feb 2018 |

Externally published | Yes |

Event | 12th International Symposium on Parameterized and Exact Computation, IPEC 2017 - Vienna, Austria Duration: 6 Sep 2017 → 8 Sep 2017 |

### Publication series

Name | Leibniz International Proceedings in Informatics, LIPIcs |
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Volume | 89 |

ISSN (Print) | 1868-8969 |

### Conference

Conference | 12th International Symposium on Parameterized and Exact Computation, IPEC 2017 |
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Country/Territory | Austria |

City | Vienna |

Period | 6/09/17 → 8/09/17 |

## Keywords

- Enumeration algorithms
- K-degenerate graphs
- Maximal cliques

## ASJC Scopus subject areas

- Software