相关论文: A refined graph container lemma and applications t…

The Hubbard model and extended Hubbard model on the honeycomb lattice can be seen as prototype models of single layer graphene placed in a high dielectric constant environment that screens the Coulomb interaction. Taking advantage of the…

We study the problem of deterministic approximate counting of matchings and independent sets in graphs of bounded connective constant. More generally, we consider the problem of evaluating the partition functions of the monomer-dimer model…

We present a simplification of Lieb's proof of the flux phase conjecture for interacting fermion systems -- such as the Hubbard model --, at half filling on a general class of graphs. The main ingredient is a procedure which transforms a…

We prove that, unless P=NP, there is no polynomial-time algorithm to approximate within some multiplicative constant the average size of an independent set in graphs of maximum degree 6. This is a special case of a more general result for…

In this paper, we presented a novel convolutional neural network framework for graph modeling, with the introduction of two new modules specially designed for graph-structured data: the $k$-th order convolution operator and the adaptive…

We show that the dimer model on a bipartite graph on a torus gives rise to a quantum integrable system of special type - a cluster integrable system. The phase space of the classical system contains, as an open dense subset, the moduli…

The local Hamiltonian problem is famously complete for the class QMA, the quantum analogue of NP. The complexity of its semi-classical version, in which the terms of the Hamiltonian are required to commute (the CLH problem), has attracted…

Graph learning (GL) can dynamically capture the distribution structure (graph structure) of data based on graph convolutional networks (GCN), and the learning quality of the graph structure directly influences GCN for semi-supervised…

The study of the existence of hamiltonian cycles in a graph is a classic problem in graph theory. By incorporating toughness and spectral conditions, we can consider Chv\'{a}tal's conjecture from another perspective: what is the spectral…

We study structural conditions in dense graphs that guarantee the existence of vertex-spanning substructures such as Hamilton cycles. It is easy to see that every Hamiltonian graph is connected, has a perfect fractional matching and,…

We prove a strengthened sector lemma for irreducible, finite-dimensional, locally finite, essential, cocompact CAT(0) cube complexes under the additional hypothesis that the complex is \emph{hyperplane-essential}; we prove that every…

We propose a novel cohesive subgraph model called $\tau$-strengthened $(\alpha,\beta)$-core (denoted as $(\alpha,\beta)_{\tau}$-core), which is the first to consider both tie strength and vertex engagement on bipartite graphs. An edge is a…

The layered graphene systems exhibit the rich and unique excitation spectra arising from the electron-electron Coulomb interactions. The generalized tight-binding model is developed to cover the planar/buckled/cylindrical structures,…

Bipartite graphs are ubiquitous across various scientific and engineering fields. Simultaneously grouping the two types of nodes in a bipartite graph via biclustering represents a fundamental challenge in network analysis for such graphs.…

Graph transformers (GTs) have emerged as a promising architecture that is theoretically more expressive than message-passing graph neural networks (GNNs). However, typical GT models have at least quadratic complexity and thus cannot scale…

We study the stable matching problem in non-bipartite graphs with incomplete but strict preference lists, where the edges have weights and the goal is to compute a stable matching of minimum or maximum weight. This problem is known to be…

We study the design of robust subexponential algorithms for classical connectivity problems on intersection graphs of similarly sized fat objects in $\mathbb{R}^d$. In this setting, each vertex corresponds to a geometric object, and two…

Previous work has suggested that the structural restrictions of graphs from classes of bounded expansion--locally dense pockets in a globally sparse graph--naturally coincide with common properties of real-world networks such as clustering…

It follows from the Marcus-Spielman-Srivastava proof of the Kadison-Singer conjecture that if $G=(V,E)$ is a $\Delta$-regular dense expander then there is an edge-induced subgraph $H=(V,E_H)$ of $G$ of constant maximum degree which is also…

While stabilizer tableaus have proven exceptionally useful as a descriptive tool for additive quantum codes, they offer little guidance for concrete constructions or coding algorithm analysis. We introduce a representation of stabilizer…