Size of the largest induced forest in subcubic graphs of girth at least four and five

Tom Kelly, Chun Hung Liu

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish (US)
Pages (from-to)457-478
Number of pages22
JournalJournal of Graph Theory
Volume89
Issue number4
DOIs
StatePublished - Dec 2018

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

Keywords

  • feedback vertex-sets
  • induced forests
  • subcubic graphs

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