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 language | English |
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Pages (from-to) | 16-22 |
Number of pages | 7 |
Journal | Journal of Combinatorial Theory, Series B |
Volume | 149 |
DOIs | |
Publication status | Published - 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