A classification of locally semicomplete digraphs

@article{BangJensen1997ACO,
  title={A classification of locally semicomplete digraphs},
  author={J{\o}rgen Bang-Jensen and Yubao Guo and Gregory Gutin and Lutz Volkmann},
  journal={Discret. Math.},
  year={1997},
  volume={167-168},
  pages={101-114}
}

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On the number of cycles in local tournaments

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TLDR
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It is shown that every k-connected locally semicomplete digraph D with minimum outdegree at least 2k and minimum indegree at least 2k − 2 has at least m = max{2, k} vertices x1, x2, , xm such that D

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A local tournament is an oriented graph in which the inset as well as the outset of each vertex induces a tournament. Local tournaments possess many properties of tournaments and have interesting

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TLDR
A new type of sufficient condition for a digraph to be Hamiltonian is described, which combines local structure of the digraph with conditions on the degrees of non-adjacent vertices.

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TLDR
A method to generate all local tournaments by performing some simple operations on some simple basic oriented graphs is described and a description of all local tournament with the same underlying proper circular are graph is obtained.