Graph neural networks (GNNs) have demonstrated promising performance across various chemistry-related tasks. However, conventional graphs only model the pairwise connectivity in molecules, failing to adequately represent higher order connections, such as m ...
This paper presents a novel distributed approach for solving AC power flow (PF) problems. The optimization problem is reformulated into a distributed form using a communication structure corresponding to a hypergraph, by which complex relationships between ...
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 ...
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 ...
With the increasing prevalence of massive datasets, it becomes important to design algorithmic techniques for dealing with scenarios where the input to be processed does not fit in the memory of a single machine. Many highly successful approaches have emer ...
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 ...
Let c denote the largest constant such that every C-6-free graph G contains a bipartite and C-4-free subgraph having a fraction c of edges of G. Gyori, Kensell and Tompkins showed that 3/8
For a graph F, we say a hypergraph H is a Berge-F if it can be obtained from F by replacing each edge of F with a hyperedge containing it. We say a hypergraph is Berge-F-saturated if it does not contain a Berge-F, but adding any hyperedge creates a copy of ...
Given a graph F, a hypergraph is a Berge-F if it can be obtained by expanding each edge in F to a hyperedge containing it. A hypergraph H is Berge-F-saturated if H does not contain a subhypergraph that is a Berge-F, but for any edge e is an element of E((H ...
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 ...
Haxell's condition [14] is a natural hypergraph analog of Hall's condition, which is a well-known necessary and sufficient condition for a bipartite graph to admit a perfect matching. That is, when Haxell's condition holds it forces the existence of a perf ...
Let d and t be fixed positive integers, and let denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem ...
Determining the size of a maximum independent set of a graph G, denoted by alpha(G), is an NP-hard problem. Therefore many attempts are made to find upper and lower bounds, or exact values of alpha(G) for special classes of graphs. This paper is aimed towa ...
In this paper, we prove several extremal results for geometrically defined hypergraphs. In particular, we establish an improved lower bound, single exponentially decreasing in k, on the best constant delta > 0 such that the vertex classes P-1,...,P-k of ev ...
Society for Industrial and Applied Mathematics2016
Let G=(V,E)G=(V,E) be a graph in which every vertex v∈Vv∈V has a weight w(v)⩾0w(v)⩾0 and a cost c(v)⩾0c(v)⩾0. Let SGSG be the family of all maximum-weight stable sets in G . For any integer d⩾0d⩾0, a minimum d-transversal in the graph G with respect to SGS ...
This thesis is devoted to crossing patterns of edges in topological graphs. We consider the following four problems: A thrackle is a graph drawn in the plane such that every pair of edges meet exactly once: either at a common endpoint or in a proper crossi ...
We consider a set V of elements and an optimization problem on V: the search for a maximum (or minimum) cardinality subset of V verifying a given property a"similar to. A d-transversal is a subset of V which intersects any optimum solution in at least d el ...
The overlap number of a finite (d + 1)-uniform hypergraph H is the largest constant c(H) is an element of (0, 1] such that no matter how we map the vertices of H into R-d, there is a point covered by at least a c(H)-fraction of the simplices induced by the ...
