Geodesic
A Sufficient Condition for Graphs to Be Super k-Restricted Edge Connected
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 537-545

Voir la notice de l'article provenant de la source Library of Science

For a subset S of edges in a connected graph G, S is a k-restricted edge cut if G − S is disconnected and every component of G − S has at least k vertices. The k-restricted edge connectivity of G, denoted by λ_k (G), is defined as the cardinality of a minimum k-restricted edge cut. Let ξ_k(G) = min{ | [ X , X ] | : |X| = k, G[X] is connected }, where X = V (G) \ X. A graph G is super k-restricted edge connected if every minimum k-restricted edge cut of G isolates a component of order exactly k. Let k be a positive integer and let G be a graph of order ν≥ 2k. In this paper, we show that if | N( u ) ∪ N( v ) | ≥ k +1 for all pairs u, v of nonadjacent vertices and ξ_k (G) ≤ ν/2+k, then G is super k-restricted edge connected.
Keywords: graph, neighborhood, k -restricted edge connectivity, super k -restricted edge connected graph 
@article{DMGT_2017_37_3_a2,
     author = {Wang, Shiying and Wang, Meiyu and Zhang, Lei},
     title = {A {Sufficient} {Condition} for {Graphs} to {Be} {Super} {k-Restricted} {Edge} {Connected}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {537--545},
     publisher = {mathdoc},
     volume = {37},
     number = {3},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a2/}
}
TY  - JOUR
AU  - Wang, Shiying
AU  - Wang, Meiyu
AU  - Zhang, Lei
TI  - A Sufficient Condition for Graphs to Be Super k-Restricted Edge Connected
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2017
SP  - 537
EP  - 545
VL  - 37
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a2/
LA  - en
ID  - DMGT_2017_37_3_a2
ER  - 
%0 Journal Article
%A Wang, Shiying
%A Wang, Meiyu
%A Zhang, Lei
%T A Sufficient Condition for Graphs to Be Super k-Restricted Edge Connected
%J Discussiones Mathematicae. Graph Theory
%D 2017
%P 537-545
%V 37
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a2/
%G en
%F DMGT_2017_37_3_a2
Wang, Shiying; Wang, Meiyu; Zhang, Lei. A Sufficient Condition for Graphs to Be Super k-Restricted Edge Connected. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 537-545. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a2/