A Note on the Vertex-Connectivity Augmentation Problem
نویسندگان
چکیده
منابع مشابه
A note on hypergraph connectivity augmentation
We prove an abstract version of an edge-splitting theorem for directed hypergraphs that appeared in [1], and use this result to obtain min-max theorems on hypergraph augmentation problems that are linked to orientations. These problems include (k, l)-edge-connectivity augmentation of directed hypergraphs, and (k, l)-partition-connectivity augmentation of undirected hypergraphs by uniform hypere...
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 کاملUndirected Vertex-Connectivity Structure and Smallest Four-Vertex-Connectivity Augmentation
In this paper we study properties for the structure of an undirected graph that is not vertex connected We also study the evolution of this structure when an edge is added to optimally increase the vertex connectivity of the underlying graph Several properties reported here can be extended to the case of a graph that is not k vertex connected for an arbitrary k Using properties obtained here we...
متن کاملA Note on Eswaran and Tarjan's Algorithm for the Strong Connectivity Augmentation Problem
In a seminal paper Eswaran and Tarjan [1] introduced several augmentation problems and presented linear time algorithms for them. This paper points out an error in Eswaran and Tarjan's algorithm for the strong connectivity augmentation problem. Consequently, the application of their algorithm can result in a network that is not strongly connected. Luckily, the error can be fixed fairly easily, ...
متن کاملIndependence Free Graphs and Vertex Connectivity Augmentation
Given an undirected graph G and a positive integer k, the k-vertex-connectivity augmentation problem is to find a smallest set F of new edges for which G + F is k-vertex-connected. Polynomial algorithms for this problem have been found only for k≤ 4 and a major open question in graph connectivity is whether this problem is solvable in polynomial time in general. In this paper we develop an algo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1997
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1786