Related papers: The Unravelling Problem
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
We present a spectral theory of hypergraphs that closely parallels Spectral Graph Theory. A number of recent developments building upon classical work has led to a rich understanding of "hyperdeterminants" of hypermatrices, a.k.a.…
This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…
This paper addresses the problem of learning an undirected graph from data gathered at each nodes. Within the graph signal processing framework, the topology of such graph can be linked to the support of the conditional correlation matrix…
We generalise the existence of combinatorial designs to the setting of subset sums in lattices with coordinates indexed by labelled faces of simplicial complexes. This general framework includes the problem of decomposing hypergraphs with…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
In this paper, we explore the graph partitioning problem, a pivotal combina-torial optimization challenge with extensive applications in various fields such as science, technology, and business. Recognized as an NP-hard prob-lem, graph…
Using derandomization, we provide an upper bound on the compression size of solutions to the graph coloring problem. In general, if solutions to a combinatorial problem exist with high probability and the probability is simple, then there…
A variant of the well-known Set Covering Problem is studied in this paper, where subsets of a collection have to be selected, and pairwise conflicts among subsets of items exist. The selection of each subset has a cost, and the inclusion of…
We examine a number of results of infinite combinatorics using the techniques of reverse mathematics. Our results are inspired by similar results in recursive combinatorics. Theorems included concern colorings of graphs and bounded graphs,…
We survey interactions between the topology and the combinatorics of complex hyperplane arrangements. Without claiming to be exhaustive, we examine in this setting combinatorial aspects of fundamental groups, associated graded Lie algebras,…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
This paper describes several new problems and ideas concerning algebraic geometry and complexity theory. It first uses the idea of coloring graphs with elements of finite fields. This procedure then shows that graph coloring problems can be…
In geometric, algebraic, and topological combinatorics, the unimodality of combinatorial generating polynomials is frequently studied. Unimodality follows when the polynomial is (real) stable, a property often deduced via the theory of…
The topic of this treatise is a combinatorial technique called Graph Pebbling. We investigate pebbling numbers, weight functions, flow networks, hypercubes, and the zero-sum conjecture of Erd\H{o}s and Lemke. This investigation is a…
As in our previous work [1] we address the problem to determine the splitting of the normal bundle of rational curves. With apolarity theory we are able to characterize some particular subvarieties in some Hilbert scheme of rational curves,…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
We study the network dismantling problem, which consists in determining a minimal set of vertices whose removal leaves the network broken into connected components of sub-extensive size. For a large class of random graphs, this problem is…
The motion of binary star systems is re-examined in the presence of perturbations from the theory of general relativity. The Kepler problem is regularized and linearized with quaternions. In this way first order perturbation results are…
The purpose of this note is to attach a name to a natural class of combinatorial problems and to point out that this class includes many important special cases. We also show that a simple problem of placing nonoverlapping labels on a…