## Abstract A __k__βking in a digraph __D__ is a vertex which can reach every other vertex by a directed path of length at most __k__. We consider __k__βkings in locally semicomplete digraphs and mainly prove that all strong locally semicomplete digraphs which are not round decomposable contain a 2
On complementary cycles in locally semicomplete digraphs
β Scribed by Yubao Guo; Lutz Volkmann
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 440 KB
- Volume
- 135
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
In this paper we show that a 2-connected locally semicomplete digraph of order at least 8 is not cycle complementary if and only if it is 2-diregular and has odd order. This result yields immediately two conjectures of Bang-Jensen.
π SIMILAR VOLUMES
The problem of finding necessary and sufficient conditions for a semicomplete multipartite digraph (SMD) to be Hamiltonian, seems to be both very interesting and difficult. Bang-Jensen, Gutin and Huang (Discrete Math to appear) proved a sufficient condition for a SMD to be Hamiltonian. A strengtheni
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