Strong subgraph k ‐connectivity
نویسندگان
چکیده
منابع مشابه
Strong Subgraph $k$-connectivity
Generalized connectivity introduced by Hager (1985) has been studied extensively in undirected graphs and become an established area in undirected graph theory. For connectivity problems, directed graphs can be considered as generalizations of undirected graphs. In this paper, we introduce a natural extension of generalized k-connectivity of undirected graphs to directed graphs (we call it stro...
متن کاملStrong subgraph $k$-connectivity bounds
Let D = (V,A) be a digraph of order n, S a subset of V of size k and 2 ≤ k ≤ n. Strong subgraphs D1, . . . , Dp containing S are said to be internally disjoint if V (Di)∩V (Dj) = S and A(Di)∩A(Dj) = ∅ for all 1 ≤ i < j ≤ p. Let κS(D) be the maximum number of internally disjoint strong digraphs containing S in D. The strong subgraph kconnectivity is defined as κk(D) = min{κS(D) | S ⊆ V, |S| = k}...
متن کاملHigh connectivity keeping connected subgraph
It was proved by Mader that, for every integer l, every k-connected graph of sufficiently large order contains a vertex set X of order precisely l such that G−X is (k − 2)-connected. This is no longer true if we require X to be connected, even for l = 3. Motivated by this fact, we are trying to find an ”obstruction” for k-connected graphs without such a connected subgraph. It turns out that the...
متن کاملSubgraph Induced Planar Connectivity Augmentation
Given a planar graph G = (V,E) and a vertex set W ⊆ V , the subgraph induced planar connectivity augmentation problem asks for a minimum cardinality set F of additional edges with end vertices in W such that G′ = (V,E∪F ) is planar and the subgraph of G′ induced by W is connected. The problem arises in automatic graph drawing in the context of c-planarity testing of clustered graphs. We describ...
متن کاملk-edge Subgraph Problems
We study here a problem on graphs that involves finding a subgraph of maximum node weights spanning up to k edges. We interpret the concept of “spanning” to mean that at least one endpoint of the edge is in the subgraph in which we seek to maximize the total weight of the nodes. We discuss the complexity of this problem and other related problems with different concepts of “spanning” and show t...
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 Graph Theory
سال: 2018
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.22437