## 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
Strongly connected orientations of mixed multigraphs
✍ Scribed by Fan R. K. Chung; Michael R. Garey; Robert E. Tarjan
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 452 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0028-3045
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📜 SIMILAR VOLUMES
We consider colorings of the directed and undirected edges of a mixed multigraph G by an ordered set of colors. We color each undirected edge in one color and each directed edge in two colors, such that the color of the first half of a directed edge is smaller than the color of the second half. The
## Abstract Suppose __G = (V, E)__ is a graph in which every vertex __x__ has a non‐negative real number __w(x)__ as its weight. The __w__‐distance sum of a vertex __y__ is __D~G, w~(y)__ = σ~x≅v~ __d(y, x)w(x).__ The __w__‐median of __G__ is the set of all vertices __y__ with minimum __w__‐distanc