## Abstract A graph __G__ = (__V__, __E__) is said to be weakly four‐connected if __G__ is 4‐edge‐connected and __G__ – __x__ is 2‐edge‐connected for every __x__ ∈ __V__. We prove that every weakly four‐connected Eulerian graph has a 2‐connected Eulerian orientation. This verifies a special case of
On some connectivity properties of Eulerian graphs
✍ Scribed by L. Lovász
- Publisher
- Akadmiai Kiad
- Year
- 1976
- Tongue
- English
- Weight
- 463 KB
- Volume
- 28
- Category
- Article
- ISSN
- 1588-2632
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📜 SIMILAR VOLUMES
## Abstract Let __v__ be an arbitrary vertex of a 4‐edge‐connected Eulerian graph __G__. First we show the existence of a nonseparating cycle decompositiion of __G__ with respect to __v__. With the help of this decomposition we are then able to construct 4 edge‐independent spanning trees with the c
The local connectivity κ(u, v) of two vertices u and v in a graph G is the maximum number of internally disjoint u-v paths in G, and the connectivity of G is defined as } for all pairs u and v of vertices in G. Let δ(G) be the minimum degree of G. We call a graph G maximally connected when κ(G) = δ
Our purpose is to consider the following conjectures: Conjecture 1 (Barneffe). . Every cubic 3-connected bipartite planar graph is Hamiltonian. Conjecture 2 (Jaeger). Every cubic cyclically 4-edge connected graph G has a cycle C such that G -V(C) is acyclic. Conjecture 3 (Jackson, Fleischner). Ever