Packing of rigid spanning subgraphs and spanning trees

Joseph Cheriyan (1) , Olivier Durand de Gevigney (2) , Zoltán Szigeti (2)

1 Combinatorics and Optimization [Waterloo]
2 G-SCOP_OC - Optimisation Combinatoire

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 án [6] providing a sufficient condition for the rigidity of a graph and a theorem of Jordán [8] on the packing of rigid spanning subgraphs. Both these results generalize the classic result of Lovász and Yemini [10] saying that every 6-connected graph is rigid. Our approach provides a transparent proof for this theorem. Our result also gives two improved upper bounds on the connectivity of graphs that have interesting properties: (1) in every 8-connected graph there exists a packing of a spanning tree and a 2-connected spanning subgraph; (2) every 14-connected graph has a 2-connected orientation.

Domaines: Recherche opérationnelle [math.OC]

Joseph Cheriyan, Olivier Durand de Gevigney, Zoltán Szigeti. Packing of rigid spanning subgraphs and spanning trees. Journal of Combinatorial Theory, Series B, 2014, 105, pp.17-25. ⟨10.1016/j.jctb.2013.11.003⟩. ⟨hal-00958668⟩