VERTICES OF OUTDEGREE k IN A MINIMALLY k-EDGE-CONNECTED DIGRAPH
Min Li · Journal of Guangxi Normal University · 2004
Let k be a positive integer,and let D be a minimally k-edge-connected simple digraph.Mader conjectured (see Combinatorics,Paul Erd(o)¨s is Eighty,Budapest,1996) that there are at least k+1 vertices of outdegree k in D.By using the so-called tree representation for any cross-free family,introduced by Edmonds et al.,in this paper,it is proved that there are at least three such vertices in D for k≥2.