id: 06091408
dt: j
an: 06091408
au: Gao, Jingzhen
ti: Lower bounds of $|X|$ and $|Y|$ of edge-cut $ (X,Y)$ and maximality and
    superiority of a digraph.
so: J. Syst. Sci. Math. Sci. 31, No. 12, 1602-1612 (2011).
py: 2011
pu: Science Press, Beijing
la: ZH
cc: 
ut: edge-cut; maximally edge-connected digraph; super-edge-connected digraph
ci: 
li: 
ab: Summary: Motivated by the existing concepts of maximally edge-connected
    digraph, super-edge-connected digraph and maximally
    local-edge-connected one, the concept of a super-local-edge-connected
    digraph is proposed. Lower bounds of $|X|$ and $|Y|$ of edge-cut $ (X,
    Y)$ with $| (X, Y)|<δ(D)$ and of nontrivial minimum edge cut $ (X, Y)$
    for arbitrary, bipartite digraphs and oriented graphs as well as ones
    with clique number at most $p$ are settled, respectively. Making use of
    them, minimum degree conditions for a digraph to be maximally
    edge-connected and super-edge-connected are derived. Analogously lower
    bounds of $|X|$ and $|Y|$ of $u-v$ edge-cut $ (X, Y)$ with $|
    (X,Y)|\leq \min \{d^+ (u), d^- (v)\}-1$ and of nontrivial minimum
    $λ(u-v)$ edge-cut are presented; and then minimum degree conditions
    for maximally local-edge-connected and super-local-edge-connected
    digraphs are obtained.
rv: