相关论文: Bipartite noisy hypercubes have large higher-order…

In a recent work (ECCC, TR18-171, 2018), we introduced models of testing graph properties in which, in addition to answers to the usual graph-queries, the tester obtains {\em random vertices drawn according to an arbitrary distribution…

As a partial answer to a question of Rao, a deterministic and customizable efficient algorithm is presented to test whether an arbitrary graphical degree sequence has a bipartite realization. The algorithm can be configured to run in…

It is well-known that eigenvalues of graphs can be used to describe structural properties and parameters of graphs. A theorem of Nosal states that if $G$ is a triangle-free graph with $m$ edges, then $\lambda (G)\le \sqrt{m}$, equality…

In the final project paper we consider a graph parameter called readability. Motivation for readability comes from bioinformatics applications. Graphs arising in problems related to genome sequencing are of small readability, which…

For discrete weighted graphs there is sufficient literature about the Cheeger cut and the Cheeger problem, but for metric graphs there are few results about these problems. Our aim is to study the Cheeger cut and the Cheeger problem in…

We develop a nonlinear spectral graph theory, in which the Laplace operator is replaced by the 1-Laplacian ?$\Delta_1$. The eigenvalue problem is to solve a nonlinear system involving a set valued function. In the study, we investigate the…

With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent…

Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…

In this paper, we study the type graph, namely, a bipartite graph induced by a joint type. We investigate the maximum edge density of induced bipartite subgraphs of this graph having a number of vertices on each side on an exponential scale…

We aim to learn a sparse and connected graph from sparse data, where the number of observations K can be substantially smaller than the signal dimension N for signals x in R^N, and the underlying distribution is unknown. In this severely…

In this paper, we study the problem of certifying whether a graph is bipartite (i.e. $2$-colorable) with a locally checkable proof (LCP) that is able to hide a $2$-coloring from the verifier. More precisely, we say an LCP for $2$-coloring…

The CHY construction naturally associates a vector in $\mathbb{R}^{(n-3)!}$ to every 2-regular graph with $n$ vertices. Partial amplitudes in the biadjoint scalar theory are given by the inner product of vectors associated with a pair of…

A fundamental problem in mathematics and network analysis is to find conditions under which a graph can be partitioned into smaller pieces. The most important tool for this partitioning is the Fiedler vector or discrete Cheeger inequality.…

While the adjacency tensor of a bipartite 2-graph is a nonnegative biquadratic tensor, it is inherently reducible. To address this limitation, we introduce the concept of quasi-irreducibility in this paper. The adjacency tensor of a…

Suppose $G$ and $H$ are bipartite graphs and $L: V(G)\to 2^{V(H)}$ induces a partition of $V(H)$ such that the subgraph of $H$ induced between $L(v)$ and $L(v')$ is a matching whenever $vv'\in E(G)$. We show for each $\varepsilon>0$ that,…

A half-square of a bipartite graph $B=(X,Y,E_B)$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. If $G=(V,E_G)$ is the half-square of a planar bipartite graph…

Bipartite graphs model the relationships between two disjoint sets of entities in several applications and are naturally drawn as 2-layer graph drawings. In such drawings, the two sets of entities (vertices) are placed on two parallel lines…

We introduce and develop equivalent spectral graph theory for several fundamental graph cut problems including maxcut, mincut, Cheeger cut, anti-Cheeger cut, dual Cheeger problem and their useful variants. A specified strategy for achieving…

Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this note, we give some different combinatorial conditions for a bipartite graph which are equal to…

The Cheeger inequality for undirected graphs, which relates the conductance of an undirected graph and the second smallest eigenvalue of its normalized Laplacian, is a cornerstone of spectral graph theory. The Cheeger inequality has been…