Size of the largest induced forest in subcubic graphs of girth at least four and five Academic Article uri icon


  • © 2018 Wiley Periodicals, Inc. 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.

author list (cited authors)

  • Kelly, T., & Liu, C.

citation count

  • 1

publication date

  • December 2018