English

Detecting and Enumerating Small Induced Subgraphs in $c$-Closed Graphs

Data Structures and Algorithms 2020-07-24 v1 Discrete Mathematics

Abstract

Fox et al. [SIAM J. Comp. 2020] introduced a new parameter, called cc-closure, for a parameterized study of clique enumeration problems. A graph GG is cc-closed if every pair of vertices with at least cc common neighbors is adjacent. The cc-closure of GG is the smallest cc such that GG is cc-closed. We systematically explore the impact of cc-closure on the computational complexity of detecting and enumerating small induced subgraphs. More precisely, for each graph HH on three or four vertices, we investigate parameterized polynomial-time algorithms for detecting HH and for enumerating all occurrences of HH in a given cc-closed graph.

Keywords

Cite

@article{arxiv.2007.12077,
  title  = {Detecting and Enumerating Small Induced Subgraphs in $c$-Closed Graphs},
  author = {Tomohiro Koana and André Nichterlein},
  journal= {arXiv preprint arXiv:2007.12077},
  year   = {2020}
}
R2 v1 2026-06-23T17:21:08.816Z