Cliques in Odd-Minor-Free Graphs

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 $n$-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 $O(n^2)$ cliques (which is tight), and conclude a $O(n^3)$ time algorithm for listing all cliques.

References in corpus (3)

• Rank-width and Tree-width of H-minor-free Graphs
• The maximum number of cliques in a graph embedded in a surface
• Faster Shortest Path Algorithm for H-Minor Free Graphs with Negative Edge Weights

Cited by in corpus (1)

• Number of cliques in graphs with a forbidden subdivision