相关论文: Sharp Davies-Gaffney-Grigor'yan Lemma on Graphs

The strong chromatic number, $\chi_S(G)$, of an $n$-vertex graph $G$ is the smallest number $k$ such that after adding $k\lceil n/k\rceil-n$ isolated vertices to $G$ and considering {\bf any} partition of the vertices of the resulting graph…

The availability of graph data with node attributes that can be either discrete or real-valued is constantly increasing. While existing kernel methods are effective techniques for dealing with graphs having discrete node labels, their…

We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be…

We consider the problem of classifying graphs using graph kernels. We define a new graph kernel, called the generalized shortest path kernel, based on the number and length of shortest paths between nodes. For our example classification…

The main challenge addressed in this paper is to identify individual terms in a superposition of heat kernels on a graph. We establish geometric conditions on the vertices at which these heat kernels are centered and find bounds on the time…

In this paper, we prove a sharp Mei's Lemma with assuming the bases of the underlying general dyadic grids are different. As a byproduct, we specify all the possible cases of adjacent general dyadic systems with different bases. The proofs…

We derive a gradient estimate for positive functions, in particular for positive solutions to the heat equation, on finite or locally finite graphs. Unlike the well known Li-Yau estimate, which is based on the maximum principle, our…

Hajnal and Szemeredi proved that every graph G with |G|=ks and minimum degree at least k(s-1) contains k vertex disjoint s-cliques; moreover this degree bound is optimal. We extend their theorem to directed graphs by showing that every…

Let $G$ be an infinite, edge- and vertex-weighted graph with certain reasonable restrictions. We construct the heat kernel of the associated Laplacian using an adaptation of the parametrix approach due to Minakshisundaram-Pleijel in the…

We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing.

We consider the Gaussian curvature conjecture of a minimal graph $S$ over the unit disk. First of all we reduce the general conjecture to the estimating the Gaussian curvature of some Scherk's type minimal surfaces over a quadrilateral…

We extend the notion of chip-firing to weighted graphs, and generalize the Greedy Algorithm and Dhar's Burning Algorithm to weighted graphs. For a vertex $q \in V(\Gamma)$, we give an upper bound for the number of linearly equivalent…

In two recent papers by Veitch and Roy and by Borgs, Chayes, Cohn, and Holden, a new class of sparse random graph processes based on the concept of graphexes over $\sigma$-finite measure spaces has been introduced. In this paper, we…

Recently, the author and Melentijevi\'c resolved the longstanding Gaussian curvature problem by proving the sharp inequality \[ |\mathcal{K}| < c_0 = \frac{\pi^2}{2} \] for minimal graphs over the unit disk, evaluated at the point of the…

Graph convolutional networks gain remarkable success in semi-supervised learning on graph structured data. The key to graph-based semisupervised learning is capturing the smoothness of labels or features over nodes exerted by graph…

We consider the asymptotics of the discrete heat kernel on isoradial graphs for the case where the time and the edge lengths tend to zero simultaneously. Depending on the asymptotic ratio between time and edge lengths, we show that two…

The degree-based entropy of a graph is defined as the Shannon entropy based on the information functional that associates the vertices of the graph with the corresponding degrees. In this paper, we study extremal problems of finding the…

We consider Kolmogorov operator $-\nabla \cdot a \cdot \nabla + b \cdot \nabla$ with measurable uniformly elliptic matrix $a$ and prove Gaussian lower and upper bounds on its heat kernel under minimal assumptions on the vector field $b$ and…

In this paper, we focus on the heat kernel estimates for diffusions and jump processes on metric measure spaces satisfying a weak chain condition, where the length of a nearly shortest $\varepsilon$-chain between two points $x,y$ is…

At low energies, electrons in doped graphene sheets are described by a massless Dirac fermion Hamiltonian. In this work we present a semi-analytical expression for the dynamical density-density linear-response function of noninteracting…