Thomassen (1991) proved that there is no degree of strong connectivity which guarantees a cycle through two given vertices in a digraph. In this paper we consider a large family of digraphs, including symmetric digraphs (i.e. digraphs obtained from undirected graphs by replacing each edge by a di
k-Linked and k-cyclic digraphs
β Scribed by Yannis Manoussakis
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 838 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0095-8956
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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.
## Abstract Recently, Mader [7] proved that every 2__k__βconnected graph with girth __g__(__G__) sufficiently large is __k__βlinked. We show here that __g__(__G__ β₯ 11 will do unless __k__β=β4,5. If __k__β=β4,5, then __g__(__G__) β₯ 19 will do. Β© 2003 Wiley Periodicals, Inc. J Graph Theory 45: 48β50