Restricted arc-connectivity of generalized p -cycles

Authors:
C. Balbuena;P. García-Vázquez;A. Hansberg;L. P. Montejano
Affiliations:
Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain;Departamento de Matemática Aplicada I, Universidad de Sevilla, Sevilla, Spain;Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain;Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain
Venue:
Discrete Applied Mathematics
Year:
2012

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Abstract

For a strongly connected digraph D the restricted arc-connectivity @l^'(D) is defined as the minimum cardinality of an arc-cut over all arc-cuts S satisfying that D-S has a non-trivial strong component D"1 such that D-V(D"1) contains an arc. In this paper we prove that a generalized p-cycle is @l^'-optimal if diam(D)@?2@?+p-2, where @? is the semigirth of D and p=3. Further we show that the k-iterated line digraph is @l^'-optimal if diam(D)@?2@?+p-2+k for p=3. We improve these results for p large enough and we also improve known results on super-@l for p-cycles with p=3.