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Connectivity properties of locally semicomplete digraphs

✍ Scribed by Yubao Guo; Lutz Volkmann


Publisher
John Wiley and Sons
Year
1994
Tongue
English
Weight
548 KB
Volume
18
Category
Article
ISSN
0364-9024

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✦ Synopsis


Abstract

It is shown that every k‐connected locally semicomplete digraph D with minimum outdegree at least 2__k__ and minimum indegree at least 2__k__ βˆ’ 2 has at least m = max{2, k} vertices x~1~, x~2~, ⃛, x~m~ such that D βˆ’ x~i~ is k‐connected for i = 1, 2, ⃛, m.


πŸ“œ SIMILAR VOLUMES


Weakly Hamiltonian-connected locally sem
✍ Bang-Jensen, JοΏ½rgen; Guo, Yubao; Volkmann, Lutz πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 630 KB

We characterize weakly hamiltonian-connected locally semicomplete digraphs.

Strongly Hamiltonian-connected locally s
✍ Guo, Yubao πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 513 KB

We give some sufficient conditions for locally semicomplete digraphs to contain a hamiltonian path from a prescribed vertex to another prescribed vertex. As an immediate consequence of these, we obtain that every 4-connected locally semicomplete digraph is strongly hamiltonian-connected. Our results

Kings in locally semicomplete digraphs
✍ Ruixia Wang; Aimin Yang; Shiying Wang πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 94 KB

## Abstract A __k__‐king 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__‐kings in locally semicomplete digraphs and mainly prove that all strong locally semicomplete digraphs which are not round decomposable contain a 2

Locally semicomplete digraphs: A general
✍ JΓΈrgen Bang-Jensen πŸ“‚ Article πŸ“… 1990 πŸ› John Wiley and Sons 🌐 English βš– 1022 KB

## Abstract In this paper we introduce a new class of directed graphs called locally semicomplete digraphs. These are defined to be those digraphs for which the following holds: for every vertex __x__ the vertices dominated by __x__ induce a semicomplete digraph and the vertices that dominate __x__

Locally semicomplete digraphs that are c
✍ Guo, Yubao; Volkmann, Lutz πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 923 KB

If A and Bare two subdigraphs of D, then we denote by &(A, 5) the distance between A and 5. Let D be a 2-connected locally semicomplete digraph on n 2 6 vertices. If S is a minimum separating set of D and d = min{do-s(N+(s) -S, N-(s) -S ) l s E S}, then rn = max(3, d + 2) I n/2 and D contains t w o

On complementary cycles in locally semic
✍ Yubao Guo; Lutz Volkmann πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 440 KB

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.