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Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...
A motif is a frequently occurring subgraph of a given directed or undirected graph G (Milo et al.). Motifs capture higher order organizational structure of G beyond edge relationships, and, therefore, have found wide applications such as in graph clusterin ...
Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study th ...
Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may offer new applicati ...
In this note, we improve on results of Hoppen, Kohayakawa and Lefmann about the maximum number of edge colorings without monochromatic copies of a star of a fixed size that a graph on n vertices may admit. Our results rely on an improved application of an ...
We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges, but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows for the generation of graphs with extens ...
In diffusion social learning over weakly-connected graphs, it has been shown recently that influential agents shape the beliefs of non-influential agents. This paper analyzes this mechanism more closely and addresses two main questions. First, the article ...
We study different symbolic algorithms to solve two related reconfiguration problems on graphs: the token swapping problem and the permutation routing via matchings problem. Input to both problems is a connected graph with labeled vertices and a token in e ...
Cographs constitute a small point in the atlas of graph classes. However, by zooming in on this point, we discover a complex world, where many parameters jump from finiteness to infinity. In the present paper, we identify several milestones in the world of ...
