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Spanning trees and spanning Eulerian subgraphs with small degrees

Hasanvand, M ; Sharif University of Technology | 2015

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  1. Type of Document: Article
  2. DOI: 10.1016/j.disc.2015.02.022
  3. Publisher: Elsevier , 2015
  4. Abstract:
  5. Liu and Xu (1998) and Ellingham, Nam and Voss (2002) independently showed that every k-edge-connected simple graph G has a spanning tree T such that for each vertex v, dT(v) ≤ ⌈ d(v)/k ⌉ + 2. In this paper we show that every k-edge-connected graph G has a spanning tree T such that for each vertex v, dT(v)≤ ⌈ d(v)-2/k ⌉ + 2; also if G has k edge-disjoint spanning trees, then T can be found such that for each vertex v, dT(v) ≤ ⌈ d(v)-1/k ⌉ + 1. This result implies that every (r-1)-edge-connected r-regular graph (with r ≥ 4) has a spanning Eulerian subgraph whose degrees lie in the set {2,4,6}; also reduces the edge-connectivity needed for some theorems due to Barát and Gerbner (2014) and Thomassen (2008, 2013). Moreover these bounds for finding spanning trees are sharp
  6. Keywords:
  7. Connectivity ; Regular graph ; Spanning Eulerian ; Spanning tree
  8. Source: Discrete Mathematics ; Volume 338, Issue 8 , August , 2015 , Pages 1317-1321 ; 0012365X (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0012365X1500093X