A Cantor-Bernstein-type theorem for spanning trees in infinite graphs

Joshua Erde, Max Pitz, Attila Joó, J Pascal Gollin, Paul Knappe

Research output: Contribution to journalArticlepeer-review

Abstract

We show that if a graph admits a packing and a covering both consisting of λ many spanning trees, where λ is some infinite cardinal, then the graph also admits a decomposition into λ many spanning trees. For finite λ the analogous question remains open, however, a slightly weaker statement is proved.

Original languageEnglish
Pages (from-to)16-22
Number of pages7
JournalJournal of Combinatorial Theory. Series B
Volume149
DOIs
Publication statusPublished - 2021

Keywords

  • Packing-Covering
  • Cantor-Bernstein theorem
  • Spanning tree
  • Packing
  • Spanning trees
  • Covering
  • Colouring number

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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