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A conjeccture concerning strongly connected graphs

โœ Scribed by Binyamin Schwarz


Book ID
104156478
Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
1014 KB
Volume
286
Category
Article
ISSN
0024-3795

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โœฆ Synopsis


In memory of my beloved wife Ruhama

Let C&KY!) b< the class of all directed gra without loops zad wilhaut m~~ti~ie arcs, such that each graph G has N vertice ci arcs. A primal subgraph of G is generated by deleting one vertex and all the a ng out from this viwex or into it. We conjecture that if G E CP(n:n). where (n(n -1)/2) + 1 <(i< n(~ -I). and if G is strongly connecter:, then it has a strongly connected primal subgraph. Skis conjecture is rified for n = 3, 4, and 5 (Theorems 1, 3' and 5). Two related results hoId for all II heorems 2 and 4).


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