β Scribed by M.D. Shklover
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## Abstract A graph is locally connected if for each vertex Ξ½ of degree __β§2__, the subgraph induced by the vertices adjacent to Ξ½ is connected. In this paper we establish a sharp threshold function for local connectivity. Specifically, if the probability of an edge of a labeled graph of order __n_
Functional connectivity between two voxels or regions of voxels can be measured by the correlation between voxel measurements from either PET CBF or BOLD fMRI images in 3D. We propose to look at the entire 6D matrix of correlations between all voxels and search for 6D local maxima. The main result i
We prove that, in a random graph with n vertices and N = cn log n edges, the subgraph generated by a set of all vertices of degree at least k + 1 is k-leaf connected for c > f . A threshold function for k-leaf connectivity is also found. ## 1. MAIN RESULTS Let G = (V(G),E(G)) be a graph, where V (