We prove that every 6k-connected graph contains k edge-disjoint rigid (and hence 2-connected) spanning subgraphs. By using this result we can settle special cases of two conjectures, due to Kriesell and Thomassen, respectively: we show that every 12-connected graph G has a spanning tree T for which G - E(T) is 2-connected, and that every 18-connected graph has a 2-connected orientation.
- 2-connected orientation
- Connectivity of graphs
- Rigidity matroid
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics