A conjeccture concerning strongly connected graphs

✍ Scribed by Binyamin Schwarz

• Book ID: 104156478
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 1014 KB
• Volume: 286
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(98)10158-1

✦ 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).