Packing of Rigid Spanning Subgraphs and Spanning Trees
Discrete Mathematics
2012-01-19 v1 Combinatorics
Abstract
We prove that every (6k + 2l, 2k)-connected simple graph contains k rigid and l connected edge-disjoint spanning subgraphs. This implies a theorem of Jackson and Jord\'an [4] and a theorem of Jord\'an [6] on packing of rigid spanning subgraphs. Both these results are generalizations of the classical result of Lov\'asz and Yemini [9] saying that every 6-connected graph is rigid for which our approach provides a transparent proof. Our result also gives two improved upper bounds on the connectivity of graphs that have interesting properties: (1) every 8-connected graph packs a spanning tree and a 2-connected spanning subgraph; (2) every 14-connected graph has a 2-connected orientation.
Keywords
Cite
@article{arxiv.1201.3727,
title = {Packing of Rigid Spanning Subgraphs and Spanning Trees},
author = {Joseph Cheriyan and Olivier Durand de Gevigney and Zoltán Szigeti},
journal= {arXiv preprint arXiv:1201.3727},
year = {2012}
}