English

Finding a maximum induced degenerate subgraph faster than 2^n

Data Structures and Algorithms 2012-08-23 v1

Abstract

In this paper we study the problem of finding a maximum induced d-degenerate subgraph in a given n-vertex graph from the point of view of exact algorithms. We show that for any fixed d one can find a maximum induced d-degenerate subgraph in randomized (2-eps_d)^n n^O(1) time, for some constant eps_d>0 depending only on d. Moreover, our algorithm can be used to sample inclusion-wise maximal induced d-degenerate subgraphs in such a manner that every such subgraph is output with probability at least (2-eps_d)^-n; hence, we prove that their number is bounded by (2-eps_d)^n.

Keywords

Cite

@article{arxiv.1208.4449,
  title  = {Finding a maximum induced degenerate subgraph faster than 2^n},
  author = {Marcin Pilipczuk and Michał Pilipczuk},
  journal= {arXiv preprint arXiv:1208.4449},
  year   = {2012}
}
R2 v1 2026-06-21T21:53:51.064Z