Strongly connected orientations of plane graphs
نویسندگان
چکیده
منابع مشابه
Strongly 2-connected orientations of graphs
We prove that a graph admits a strongly 2-connected orientation if and only if it is 4-edge-connected, and every vertex-deleted subgraph is 2-edge-connected. In particular, every 4-connected graph has such an orientation while no cubic 3-connected graph has such an orientation.
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The cell rotation graph D(G) on the strongly connected orientations of a 2-edge-connected plane graph G is de5ned. It is shown that D(G) is a directed forest and every component is an in-tree with one root; if T is a component of D(G), the reversions of all orientations in T induce a component of D(G), denoted by T−, thus (T; T−) is called a pair of in-trees of D(G); G is Eulerian if and only i...
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A graph G = (V,E) is said to be weakly four-connected if G is 4-edgeconnected 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 a conjecture of A. Frank.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.08.004