Packing spanning trees and spanning 2-connected k-edge-connected essentially $$(2k-1)$$ ( 2 k - 1 ) -edge-connected subgraphs

Xiaofeng Gu ()
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Xiaofeng Gu: University of West Georgia

Journal of Combinatorial Optimization, 2017, vol. 33, issue 3, No 7, 924-933

Abstract: Abstract Let $$k\ge 2, p\ge 1, q\ge 0$$ k ≥ 2 , p ≥ 1 , q ≥ 0 be integers. We prove that every $$(4kp-2p+2q)$$ ( 4 k p - 2 p + 2 q ) -connected graph contains p spanning subgraphs $$G_i$$ G i for $$1\le i\le p$$ 1 ≤ i ≤ p and q spanning trees such that all $$p+q$$ p + q subgraphs are pairwise edge-disjoint and such that each $$G_i$$ G i is k-edge-connected, essentially $$(2k-1)$$ ( 2 k - 1 ) -edge-connected, and $$G_i -v$$ G i - v is $$(k-1)$$ ( k - 1 ) -edge-connected for all $$v\in V(G)$$ v ∈ V ( G ) . This extends the well-known result of Nash-Williams and Tutte on packing spanning trees, a theorem that every 6p-connected graph contains p pairwise edge-disjoint spanning 2-connected subgraphs, and a theorem that every $$(6p+2q)$$ ( 6 p + 2 q ) -connected graph contains p spanning 2-connected subgraphs and q spanning trees, which are all pairwise edge-disjoint. As an application, we improve a result on k-arc-connected orientations.

Keywords: Spanning tree; Essentially connected; Orientation; k-Rigid (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-016-0014-z

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