## Abstract By Petersen's theorem, a bridgeless cubic graph has a 2‐factor. H. Fleischner extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has a spanning even subgraph. Our main result is that, under the stronger hypothesis of 3‐edge‐connec
Spanning Eulerian Subgraphs of 2-Edge-Connected Graphs
✍ Scribed by Xiangwen Li, Chunxiang Wang, Qiong Fan, Zhaohong Niu…
- Book ID
- 120788662
- Publisher
- Springer Japan
- Year
- 2011
- Tongue
- English
- Weight
- 167 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0911-0119
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This paper studies the NP-hard problem of ÿnding a minimum size 2-edge connected spanning subgraph (2-ECSS). An algorithm is given that on an r-edge connected input graph G =(V; E) ÿnds a 2-ECSS of size at most |V |+(|E|-|V |)=(r -1). For r-regular, r-edge connected input graphs for r = 3, 4, 5 and
## Abstract It is shown that a connected graph __G__ spans an eulerian graph if and only if __G__ is not spanned by an odd complete bigraph __K__(2~m~ + 1, 2__n__ + 1). A disconnected graph spans an eulerian graph if and only if it is not the union of the trivial graph with a complete graph of odd
## Abstract In this paper, we show that if __G__ is a 3‐edge‐connected graph with $S \subseteq V(G)$ and $|S| \le 12$, then either __G__ has an Eulerian subgraph __H__ such that $S \subseteq V(H)$, or __G__ can be contracted to the Petersen graph in such a way that the preimage of each vertex of th
We prove that every planar 3-connected graph has a 2-connected spanning subgraph of maximum valence 15 . We give an example of a planar 3 -connected graph with no spanning 2-connected subgraph of maximum valence five. i) 1994 Academic Press, Inc.