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

abstract

  • AbstractIn 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 2connected subcubic graph on n vertices and m edges with girth at least four or five, respectively, has an induced forest on at least or 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 2connected graphs. Equivalently, we prove that such graphs admit feedback vertex sets with size at most or , respectively. Those exceptional graphs will be explicitly constructed, and our result can be easily modified to drop the 2connectivity requirement.

published proceedings

  • JOURNAL OF GRAPH THEORY

altmetric score

  • 0.5

author list (cited authors)

  • Kelly, T., & Liu, C.

citation count

  • 5

complete list of authors

  • Kelly, Tom||Liu, Chun-Hung

publication date

  • December 2018

publisher