9-Shredders in 9-connected graphs
نویسندگان
چکیده
For a graph G, a subset S of V (G) is called a shredder if G − S consists of three or more components. We show that if G is a 9-connected graph of order at least 67, then the number of shredders of cardinality 9 of G is less than or equal to (2|V (G)| − 9)/3. AMS 2010 Mathematics Subject Classification. 05C40
منابع مشابه
10-Shredders in 10-Connected Graphs
For a graph G, a subset S of V (G) is called a shredder if G− S consists of three or more components. We show that if G is a 10-connected graph of order at least 4227, then the number of shredders of cardinality 10 of G is less than or equal to (2|V (G)| − 11)/3.
متن کامل8-Shredders in 8-Connected Graphs
For a graph G, a subset S of V (G) is called a shredder if G − S consists of three or more components. We show that if G is an 8-connected graph of order at least 177, then the number of shredders of cardinality 8 of G is less than or equal to (2|V (G)| − 10)/3.
متن کامل(t, k)-Shredders in k-Connected Graphs
Let t, k be integers with t ≥ 3 and k ≥ 1. For a graph G, a subset S of V (G) with cardinality k is called a (t, k)-shredder if G−S consists of t or more components. In this paper, we show that if t ≥ 3, 2(t−1) ≤ k ≤ 3t−5 and G is a k-connected graph of order at least k, then the number of (t, k)-shredders of G is less than or equal to ((2t−1)(|V (G)|−f(|V (G)|)))/(2(t−1)), where f(n) denotes t...
متن کاملOn shredders and vertex connectivity augmentation
We consider the following problem: given a k-(node) connected graph G find a smallest set F of new edges so that the graph G + F is (k + 1)-connected. The complexity status of this problem is an open question. The problem admits a 2approximation algorithm. Another algorithm due to Jordán computes an augmenting edge set with at most d(k− 1)/2e edges over the optimum. C ⊂ V (G) is a k-separator (...
متن کاملOn the number of shredders
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 1]. If G contains no meshing shredders (in particular if k 3), the sharp upper bound b(n ? k ? 1)=2c is proven.
متن کامل