Large induced forests in sparse graphs

Noga Alon, Dhruv Mubayi, Robin Thomas

Research output: Contribution to journalArticlepeer-review

36 Scopus citations


For a graph G, let a(G) denote the maximum size of a subset of vertices that induces a forest. Suppose that G is connected with n vertices, e edges, and maximum degree Δ. Our results include: (a) if Δ ≤ 3, and G ≠ K4, then a(G) ≥ n- e/4 - 1/4 and this is sharp for all permissible e ≡ 3 (mod 4); and (b) if Δ ≥ 3, then a(G) ≥ α(G) + (n - α(G))/(Δ - 1)2. Several problems remain open.

Original languageEnglish (US)
Pages (from-to)113-123
Number of pages11
JournalJournal of Graph Theory
Issue number3
StatePublished - Nov 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


  • D-degenerate graph
  • Induced forests


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