We analyze the convergence of the spectrum of large random graphs to the spectrum of a limit infinite graph. We apply these results to graphs converging locally to trees and deri...
Consider random regular graphs of order n and degree d = d(n) 3. Let g = g(n) 3 satisfy (d-1)2g-1 = o(n). Then the number of cycles of lengths up to g have a distribution simila...
Brendan D. McKay, Nicholas C. Wormald, Beata Wysoc...
In the recently introduced model for cleaning a graph with brushes, we use a degree-greedy algorithm to clean a random d-regular graph on n vertices (with dn even). We then use a d...
Margaret-Ellen Messinger, Pawel Pralat, Richard J....
: The decycling number (G) of a graph G is the smallest number of vertices which can be removed from G so that the resultant graph contains no cycles. In this paper, we study the d...
Abstract. The regularization functional induced by the graph Laplacian of a random neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying ma...