An Efficient Algorithm for Enumerating Induced Subgraphs with Bounded Degeneracy

  • Kunihiro WasaEmail author
  • Takeaki Uno
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11346)


We propose a polynomial delay and polynomial space algorithm for the enumeration of k-degenerate induced subgraphs in a given graph. A graph G is k-degenerate if each of its induced subgraphs has a vertex of degree at most k. The degeneracy is considered as an indicator of the sparseness of the graph. Real-world graphs such as road networks, social networks and internet networks often have small degeneracy. Compared to other kinds of graph classes, bounded degeneracy does not give many structural properties such as induced subgraph free, or minor free. From this, using bounded degeneracy to reduce the time complexity is often not trivial. In this paper, we investigate ways of handling the degeneracy and propose an efficient algorithm for the k-degenerate induced subgraph enumeration. The time complexity is \(\mathcal {O}\left( \min \left\{ \varDelta + kk', (k')^2\right\} \right) \) time per solution with polynomial preprocessing time and the space complexity is linear in the input graph size, where \(\varDelta \) and \(k'\) are the maximum degree and the degeneracy of the input graph.


Graph algorithms Enumeration algorithms Polynomial delay k-degenerate graphs 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.National Institute of InformaticsTokyoJapan

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