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On the Asymptotic Connectivity of Random Networks under the Random Connection Model
Asymptotic Connectivity Random Networks Random Connection Model
2011/3/4
Consider a network where all nodes are distributed on a unit square following a Poisson distribution with known density and a pair of nodes separated by an Euclidean distance x are directly connecte...
The rainbow connectivity of Cayley graphs of Abelian groups
The rainbow connectivity Cayley graphs of Abelian groups
2010/11/9
A path in an edge-colored graph $G$, where adjacent edges may have the same color, is called a rainbow path if no two edges of the path are colored the same. The rainbow connectivity $rc(G)$ of $G$ i...
Connectivity and Minimal Distance Spectral Radius of Graphs
Connectivity Spectral Radius of Graphs
2010/11/15
In this paper, we study how the distance spectral radius behaves when the graph is perturbed by grafting edges. As applications, we also determine the graph with $k$ cut vertices (respectively, $k$ cu...
The word problem and the Aharoni-Berger-Ziv conjecture on the connectivity of independence complexes
Graphs independence complexes topological connectivity algorithm
2010/12/9
For each finite simple graph G, Aharoni, Berger and Ziv consider a recur-sively defined number (G) 2 Z [ {+1} which gives a lower bound for the topological connectivity of the independence complex IG...
Simulating Undirected st-Connectivity Algorithms on Uniform JAGs and NNJAGs
Simulating Undirected st-Connectivity
2012/11/29
In a breakthrough result, Reingold showed that the Undirected st-Connectivity problem can be solved in O(log n) space. The next major challenge in this direction is whether one can extend it to direct...