Spanning trees without adjacent vertices of degree 2

Kasper Szabo Lyngsie*, Martin Merker

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Albertson, Berman, Hutchinson, and Thomassen showed in 1990 that there exist highly connected graphs in which every spanning tree contains vertices of degree 2. Using a result of Alon and Wormald, we show that there exists a natural number d such that every graph of minimum degree at least d contains a spanning tree without adjacent vertices of degree 2. Moreover, we prove that every graph with minimum degree at least 3 has a spanning tree without three consecutive vertices of degree 2.
Original languageEnglish
Article number111604
JournalDiscrete Mathematics
Issue number12
Number of pages11
Publication statusPublished - 2019


  • Spanning trees
  • Homeomorphically irreducible spanning
  • Trees
  • Non-separating cycles

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