Chapter

Algorithms - ESA 2014

Volume 8737 of the series Lecture Notes in Computer Science pp 418-429

Amortized \(\tilde{O}(|V|)\)-Delay Algorithm for Listing Chordless Cycles in Undirected Graphs

  • Rui FerreiraAffiliated withMicrosoft Bing
  • , Roberto GrossiAffiliated withUniversità di Pisa
  • , Romeo RizziAffiliated withUniversità di Verona
  • , Gustavo SacomotoAffiliated withINRIA Grenoble Rhône-AlpesUMR CNRS 5558 - LBBE, Université Lyon 1
  • , Marie-France SagotAffiliated withINRIA Grenoble Rhône-AlpesUMR CNRS 5558 - LBBE, Université Lyon 1

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Abstract

Chordless cycles are very natural structures in undirected graphs, with an important history and distinguished role in graph theory. Motivated also by previous work on the classical problem of listing cycles, we study how to list chordless cycles. The best known solution to list all the C chordless cycles contained in an undirected graph G = (V,E) takes O(|E|2 + |E| ·C) time. In this paper we provide an algorithm taking \(\tilde{O}(|E| + |V| \cdot C)\) time. We also show how to obtain the same complexity for listing all the P chordless st-paths in G (where C is replaced by P).