相关论文: The Cut Method on Hypergraphs for the Wiener Index

Cuts in graphs are a fundamental object of study, and play a central role in the study of graph algorithms. The problem of sparsifying a graph while approximately preserving its cut structure has been extensively studied and has many…

Data extraction algorithms on data hypercubes, or datacubes, are traditionally only capable of cutting boxes of data along the datacube axes. For many use cases however, this is not a sufficient approach and returns more data than users…

The von Neumann graph entropy (VNGE) can be used as a measure of graph complexity, which can be the measure of information divergence and distance between graphs. However, computing VNGE is extensively demanding for a large-scale graph. We…

Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…

A method for considering a weighted directed graph with an accuracy of up to a given partition of the set of vertices is proposed. The resulting digraph (the splitting graph) does not contain arcs inside each partition element, and the arcs…

Let $H$ be a fixed undirected graph on $k$ vertices. The $H$-hitting set problem asks for deleting a minimum number of vertices from a given graph $G$ in such a way that the resulting graph has no copies of $H$ as a subgraph. This problem…

The construction of cut trees (also known as Gomory-Hu trees) for a given graph enables the minimum-cut size of the original graph to be obtained for any pair of vertices. Cut trees are a powerful back-end for graph management and mining,…

Efficient algorithms are presented for constructing spanners in geometric intersection graphs. For a unit ball graph in R^k, a (1+\epsilon)-spanner is obtained using efficient partitioning of the space into hypercubes and solving…

Discovering the underlying structures present in large real world graphs is a fundamental scientific problem. In this paper we show that a graph's clique tree can be used to extract a hyperedge replacement grammar. If we store an ordering…

The Wiener index of a strong digraph $D$ is defined as the sum of the distances between all ordered pairs of vertices. This definition has been extended to digraphs that are not necessarily strong by defining the distance from a vertex $a$…

The Wiener index, $W(G)$, of a connected graph $G$ is the sum of distances between its vertices. In 2021, Akhmejanova et al. posed the problem of finding graphs $G$ with large $R_m(G)= |\{v\in V(G)\,|\,W(G)-W(G-v)=m \in \mathbb{Z} \}|/…

We show that Edge Multiway Cut (also called Multiterminal Cut) and Node Multiway Cut are NP-complete on graphs of maximum degree $3$ (also known as subcubic graphs). This improves on a previous degree bound of $11$. Our NP-completeness…

Consider the following "local" cut-detection problem in a directed graph: We are given a starting vertex $s$ and need to detect whether there is a cut with at most $k$ edges crossing the cut such that the side of the cut containing $s$ has…

We solve the graph bi-partitioning problem in dense graphs with arbitrary degree distribution using the replica method. We find the cut-size to scale universally with <k^1/2>. In contrast, earlier results studying the problem in graphs with…

Hypergraphs are a useful abstraction for modeling multiway relationships in data, and hypergraph clustering is the task of detecting groups of closely related nodes in such data. Graph clustering has been studied extensively, and there are…

We study the integral and measure theory of the ultraproduct of finite sets. As a main application we construct limit objects for hypergraph sequences. We give a new proof for the Hypergraph Removal Lemma and the Hypergraph Regularity…

There is a graph reduction system so that every optimal 1-planar graph can be reduced to an irreducible extended wheel graph, provided the reductions are applied such that the given graph class is preserved. A graph is optimal 1-planar if…

The paper deals with some spectral properties of (mostly infinite) quantum and combinatorial graphs. Quantum graphs have been intensively studied lately due to their numerous applications to mesoscopic physics, nanotechnology, optics, and…

In this paper we develop a framework to study observability for uniform hypergraphs. Hypergraphs, being extensions of graphs, allow edges to connect multiple nodes and unambiguously represent multi-way relationships which are ubiquitous in…

We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…