Expanding graphs, Ramanujan graphs, and 1-factor perturbations
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Given two graphs H and F, the maximum possible number of copies of H in an F-free graph on n vertices is denoted by ex(n, H, F). We investigate the function ex(n, H, kF), where kF denotes k vertex disjoint copies of a fixed graph F. Our results include cas ...
How does coarsening affect the spectrum of a general graph? We provide conditions such that the principal eigenvalues and eigenspaces of a coarsened and original graph Laplacian matrices are close. The achieved approximation is shown to depend on standard ...
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communication and ...
The lack of a formal link between neural network structure and its emergent function has hampered our understanding of how the brain processes information. We have now come closer to describing such a link by taking the direction of synaptic transmission i ...
Given a graph H and a set of graphs F, let ex(n, H, F) denote the maximum possible number of copies of H in an T-free graph on n vertices. We investigate the function ex(n, H, F), when H and members of F are cycles. Let C-k denote the cycle of length k and ...
In this note, we use methods from spectral graph theory to obtain bounds on the number of incidences between k-planes and h-planes in F-q(d), which generalizes a recent result given by Bennett, Iosevich, and Pakianathan (2014). More precisely, we prove tha ...
An abstract topological graph (briefly an AT-graph) is a pair A = (G, X) where G = (V, E) is a graph and X. E2 is a set of pairs of its edges. The AT-graph A is simply realizable if G can be drawn in the plane so that each pair of edges from X crosses exac ...
A sparsifier of a graph G (Bencztir and Karger; Spielman and Teng) is a sparse weighted subgraph (G) over tilde that approximately retains the same cut structure of G. For general graphs, non-trivial sparsification is possible only by using weighted graphs ...
