2017/11/30 by González-Moreno, D., Ortiz, R. Hernández
#05C40 05C20 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1711.11517
Let D be a strongly connected digraph. An arc set S of D is a restricted arc-cut of D if D-S has a non-trivial strong component D1 such that D-V(D1) contains an arc. The restricted arc-connectivity λ'(D) of a digraph D is the minimum cardinality over all restricted arc-cuts of D. A strongly connected digraph D is λ'-connected when λ'(D) exists. This paper presents a family \calF of strong digraphs of girth four that are not λ'-connected and for every strong digraph D∉ \calF with girth four it follows that it is λ'-connected. Also, an upper and lower bound for λ'(D) are given.