English

Cliques in Odd-Minor-Free Graphs

Combinatorics 2012-02-09 v2

Abstract

This paper is about: (1) bounds on the number of cliques in a graph in a particular class, and (2) algorithms for listing all cliques in a graph. We present a simple algorithm that lists all cliques in an nn-vertex graph in O(n) time per clique. For O(1)-degenerate graphs, such as graphs excluding a fixed minor, we describe a O(n) time algorithm for listing all cliques. We prove that graphs excluding a fixed odd-minor have O(n2)O(n^2) cliques (which is tight), and conclude a O(n3)O(n^3) time algorithm for listing all cliques.

Keywords

Cite

@article{arxiv.1108.2949,
  title  = {Cliques in Odd-Minor-Free Graphs},
  author = {Ken-ichi Kawarabayashi and David R. Wood},
  journal= {arXiv preprint arXiv:1108.2949},
  year   = {2012}
}
R2 v1 2026-06-21T18:50:28.418Z