Super edge-connectivity of de bruijn and kautz undirected graphs

2004 ◽  
Vol 19 (4) ◽  
pp. 449-454
Author(s):  
Junming Xu ◽  
Yingmei Fan
Keyword(s):  
Undirected Graphs ◽  
Edge Connectivity ◽  
De Bruijn

scholarly journals Space-Efficient Fully Dynamic DFS in Undirected Graphs †

Algorithms ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 52 ◽  
Author(s):  
Kengo Nakamura ◽  
Kunihiko Sadakane
Keyword(s):  
Undirected Graph ◽  
Undirected Graphs ◽  
Edge Connectivity ◽  
Worst Case ◽  
Depth First Search ◽  
Insertions And Deletions ◽  
Adjacency List ◽  
Graph Traversal ◽  
Dynamic Connectivity ◽  
Traversal Algorithm

Depth-first search (DFS) is a well-known graph traversal algorithm and can be performed in O ( n + m ) time for a graph with n vertices and m edges. We consider the dynamic DFS problem, that is, to maintain a DFS tree of an undirected graph G under the condition that edges and vertices are gradually inserted into or deleted from G. We present an algorithm for this problem, which takes worst-case O ( m n · polylog ( n ) ) time per update and requires only ( 3 m + o ( m ) ) log n bits of space. This algorithm reduces the space usage of dynamic DFS algorithm to only 1.5 times as much space as that of the adjacency list of the graph. We also show applications of our dynamic DFS algorithm to dynamic connectivity, biconnectivity, and 2-edge-connectivity problems under vertex insertions and deletions.

Connectivity

2013 ◽  
pp. 37-47
Author(s):  
Mahtab Hosseininia ◽  
Faraz Dadgostari
Keyword(s):  
Connected Graph ◽  
Directed Graphs ◽  
Graph Connectivity ◽  
Breadth First Search ◽  
Undirected Graphs ◽  
Vertex Connectivity ◽  
Edge Connectivity ◽  
Graph Traversal ◽  
Path Component ◽  
Block Tree

In this chapter, the concept of graph connectivity is introduced. In the first section, some concepts such as walk, path, component and connected graph are defined, and connectedness of a graph from the viewpoint of vertex connectivity, and also, edge connectivity are discussed. Then, blocks and block tree of graphs are illustrated. In addition, connectivity in directed graphs is introduced. Furthermore, in the last section, two graph traversal algorithms, depth first search and breadth first search, are described to investigate the connectedness of directed and undirected graphs.

scholarly journals Minimum Augmentation of Edge-Connectivity between Vertices and Sets of Vertices in Undirected Graphs

Algorithmica ◽  
2008 ◽  
Vol 56 (4) ◽  
pp. 413-436 ◽  
Author(s):  
Toshimasa Ishii ◽  
Yoko Akiyama ◽  
Hiroshi Nagamochi
Keyword(s):  
Undirected Graphs ◽  
Edge Connectivity
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