Finding Independent Sets in Triangle-Free Graphs

Abstract

Finding a maximum independent set in a graph is well known to be an $NP$-complete problem. Here an $O(n^2)$-time algorithm that finds an independent set of order at least $(6n-m)/13$ in a triangle-free graph with $n$ vertices and $m$ edges is presented. A tight lower bound on independence in 4-regular triangle-free graphs is $4n/13$, so the bound is sharp for this class.