In this article, we address the maximum number of vertices of induced forests in subcubic graphs with girth at least four or five. We provide a unified approach to prove that every 2-connected subcubic graph on n vertices and m edges with girth at least four or five, respectively, has an induced forest on at least n - 2/9m or n - 1/5m vertices, respectively, except for finitely many exceptional graphs. Our results improve a result of Liu and Zhao and are tight in the sense that the bounds are attained by infinitely many 2-connected graphs. Equivalently, we prove that such graphs admit feedback vertex sets with size at most 2/9m or 1/5m, respectively. Those exceptional graphs will be explicitly constructed, and our result can be easily modified to drop the 2-connectivity requirement.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- feedback vertex-sets
- induced forests
- subcubic graphs