TY - JOUR

T1 - On the number of shredders

AU - Jordán, Tibor

PY - 1999/7

Y1 - 1999/7

N2 - A subset S of k vertices in a k-connected graph G is a shredder, if G - S has at least three components. We show that if G has n vertices, then the number of shredders is at most n, which was conjectured by Cheriyan and Thurimella [Cheriyan & Thurimella, Proc 28th Ann ACM Symp, 1996]. If G contains no meshing shredders (in particular, if k ≤ 3), the sharp upper bound [(n - k - 1)/2] is proven.

AB - A subset S of k vertices in a k-connected graph G is a shredder, if G - S has at least three components. We show that if G has n vertices, then the number of shredders is at most n, which was conjectured by Cheriyan and Thurimella [Cheriyan & Thurimella, Proc 28th Ann ACM Symp, 1996]. If G contains no meshing shredders (in particular, if k ≤ 3), the sharp upper bound [(n - k - 1)/2] is proven.

KW - Connectivity

KW - Minimum cuts

KW - k-connected graphs

UR - http://www.scopus.com/inward/record.url?scp=0033468580&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033468580&partnerID=8YFLogxK

U2 - 10.1002/(SICI)1097-0118(199907)31:3<195::AID-JGT4>3.0.CO;2-E

DO - 10.1002/(SICI)1097-0118(199907)31:3<195::AID-JGT4>3.0.CO;2-E

M3 - Article

AN - SCOPUS:0033468580

VL - 31

SP - 195

EP - 200

JO - Journal of Graph Theory

JF - Journal of Graph Theory

SN - 0364-9024

IS - 3

ER -