We show that for any vertex \(x\) of a \(d\)-regular bipartite digraph there are a vertex \(y\), in the other class of the bipartition, and \(d(x, y)\)-paths and \(d(y, x)\)-paths such that all \(2 d\) of them are pairwise arc-disjoint. This result generalizes a theorem of Hamidoune and Las Vergnas
Degree and local connectivity in digraphs
β Scribed by W. Mader
- Book ID
- 110564423
- Publisher
- Springer-Verlag
- Year
- 1985
- Tongue
- English
- Weight
- 289 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0209-9683
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## Abstract It is shown that every __k__βconnected locally semicomplete digraph __D__ with minimum outdegree at least 2__k__ and minimum indegree at least 2__k__ β 2 has at least __m__ = max{2, __k__} vertices __x__~1~, __x__~2~, β, __x__~__m__~ such that __D__ β __x__~__i__~ is __k__βconnected for
We characterize weakly hamiltonian-connected locally semicomplete digraphs.
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