An improved bound on the largest induced forests for triangle-free planar graphs

Abstract

We proved that every planar triangle-free graph of order n has a subset of vertices that induces a forest of size at least (71n + 72)/128. This improves the earlier work of Salavatipour (2006). We also pose some questions regarding planar graphs of higher girth. 1365-8050 © 2010 Discrete Mathematics and Theoretical Computer Science (DMTCS), Nancy, France.