Related papers: Cheeger inequalities for graph limits
We generalize the notion of quasirandom which concerns a class of equivalent properties that random graphs satisfy. We show that the convergence of a graph sequence under the spectral distance is equivalent to the convergence using the…
We describe a correspondence between GL_n-invariant tensors and graphs, and show how this correspondence accomodates various types of symmetries and orientations.
In this paper we study a partially overdetermined mixed boundary value problem for domains $\Omega$ contained in an unbounded set $\mathcal C$. We introduce the notion of Cheeger set relative to $\mathcal C$ and show that if a domain…
We study four different notions of convergence for graphexes, recently introduced by Borgs, Chayes, Cohn and Holden, and by Veitch and Roy. We give some properties of them and some relations between them. We also extend results by Veitch…
Graph transformers are a recent advancement in machine learning, offering a new class of neural network models for graph-structured data. The synergy between transformers and graph learning demonstrates strong performance and versatility…
We establish splitter theorems for graph immersions for two families of graphs, $k$-edge-connected graphs, with $k$ even, and 3-edge-connected, internally 4-edge-connected graphs. As a corollary, we prove that every $3$-edge-connected,…
Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…
We derive here the Friedland-Tverberg inequality for positive hyperbolic polynomials. This inequality is applied to give lower bounds for the number of matchings in $r$-regular bipartite graphs. It is shown that some of these bounds are…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
The class of 2-interval graphs has been introduced for modelling scheduling and allocation problems, and more recently for specific bioinformatic problems. Some of those applications imply restrictions on the 2-interval graphs, and justify…
We construct two minimal Cheeger sets in the Euclidean plane, i.e. unique minimizers of the ratio "perimeter over area" among their own measurable subsets. The first one gives a counterexample to the so-called weak regularity property of…
Bounds are proved for the connective constant \mu\ of an infinite, connected, \Delta-regular graph G. The main result is that \mu\ \ge \sqrt{\Delta-1} if G is vertex-transitive and simple. This inequality is proved subject to weaker…
We prove an inequality involving the degeneracy, the cutwidth and the sparsity of graphs. It implies a quadratic lower bound on the cutwidth in terms of the degeneracy for all graphs and an improvement of it for clique-free graphs.
In this work we investigate Cauchy problem and initial boundary value problem for time-fractional Airy equation on the graphs with infinite and finite bonds. We studied properties of potentials for this equation and using these properties…
We study the spectral aspects of the graph limit theory. We give a description of graphon convergence in terms of converegnce of eigenvalues and eigenspaces. Along these lines we prove a spectral version of the strong regularity lemma.…
We find closed form formulas for Kemeny's constant and its relationship with two Kirchhoffian indices for some composite graphs that use as basic building block a graph endowed with one of several symmetry properties.
In this article, we first introduce the concepts of vector fields and their divergence, and we recall the concepts of the gradient, Laplacian operator, Cheeger constants, eigenvalues, and heat kernels on a locally finite graph $V$. We give…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
Spectral partitioning is a simple, nearly-linear time, algorithm to find sparse cuts, and the Cheeger inequalities provide a worst-case guarantee for the quality of the approximation found by the algorithm. Local graph partitioning…
We study Cheeger and $p$-eigenvalue partition problems depending on a given evaluation function $\Phi$ for $p\in[1,\infty)$. We prove existence and regularity of minima, relations among the problems, convergence, and stability with respect…