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On the Existence of Noncritical Vertices in Digraphs

✍ Scribed by Nenashev, G. V.

Book ID
121571426
Publisher
Springer US
Year
2014
Tongue
English
Weight
255 KB
Volume
196
Category
Article
ISSN
1573-8795

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πŸ“œ SIMILAR VOLUMES

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## Abstract Let |__D__| and |D|^+^~__n__~ denote the number of vertices of __D__ and the number of vertices of outdegree __n__ in the digraph __D__, respectively. It is proved that every minimally __n__‐connected, finite digraph __D__ has |D|^+^~__n__~ β‰₯ __n__ + 1 and that for __n__ β‰₯ 2, there is a

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In this paper we present some results on the existence of /c-kernels and (k, [)-kernels in digraphs which generalize the following Theorem of P. Duchet [2]: "If every directed cycle of odd length in a digraph D has at least two symmetrical arcs, then D has a kernel.

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## We enumerate, up to isomorphism, several classes of labeled vertex-transitive digraphs with a prime number of vertices. There are many unsolvedi enumeration problems stated in [S]. Recently, Robinson in [8] posed more enumeration problems. Here, we give some partial answer to the problems posed