Packing of 2-Connected Spanning Subgraphs and Spanning Trees
نویسندگان
چکیده
We prove that every (6k + 2`, 2k)-connected simple graph contains k rigid and ` connected edgedisjoint spanning subgraphs. This implies a theorem of Jackson and Jordán [4] and a theorem of Jordán [6] on packing of rigid spanning subgraphs. Both these results are generalizations of the classical result of Lovász 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.
منابع مشابه
Packing of rigid spanning subgraphs and spanning trees
We prove that every (6k + 2`, 2k)-connected simple graph contains k rigid and ` connected edge-disjoint spanning subgraphs. This implies a theorem of Jackson and Jordán [4] and a theorem of Jordán [6] on packing of rigid spanning subgraphs. Both these results are generalizations of the classical result of Lovász and Yemini [9] saying that every 6-connected graph is rigid for which our approach ...
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