## Abstract It is well known that certain graphβtheoretic extremal questions play a central role in the study of communication network vulnerability. Herein we consider a generalization of some of the classical results in this area. We define a (__p__, Ξ, Ξ΄, Ξ») graph as a graph having __p__ points,
Graph decomposition with constraints on the connectivity and minimum degree
β Scribed by Carsten Thomassen
- Publisher
- John Wiley and Sons
- Year
- 1983
- Tongue
- English
- Weight
- 145 KB
- Volume
- 7
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
For each pair s,t of natural numbers there exist natural numbers f(s,t) and g(s,t) such that the vertex set of each graph of connectivity at least f(s,t) (respectively minimum degree at least g(s,t)) has a decomposition into sets which induce subgraphs of connectivity (respectively minimum degree) at least s and t, respectively.
π SIMILAR VOLUMES
## Abstract Using the wellβknown Theorem of TurΓ‘n, we present in this paper degree sequence conditions for the equality of edgeβconnectivity and minimum degree, depending on the clique number of a graph. Different examples will show that these conditions are best possible and independent of all the
In this paper, we study the inapproximability of several well-known optimization problems in network optimization. We show-that the max directed vertex-disjoint paths problem cannot be approximated within ratio 2 log 1&= n unless NP DTIME[2 polylog n ], the max directed edge-disjoint paths problem c