离散数学

In line with the recent development in topological graph theory, we are considering undirected graphs that are allowed to contain {\em multiple edges}, {\em loops}, and {\em semi-edges}. A graph is called {\em simple} if it contains no…

Network flows over time are a fascinating generalization of classical (static) network flows, introducing an element of time. They naturally model problems where travel and transmission are not instantaneous and flow may vary over time. Not…

A homomorphism from a graph $G$ to a graph $H$ is an edge-preserving mapping from $V(G)$ to $V(H)$. In the graph homomorphism problem, denoted by $Hom(H)$, the graph $H$ is fixed and we need to determine if there exists a homomorphism from…

We present a rigorous and precise analysis of the maximum degree and the average degree in a dynamic duplication-divergence graph model introduced by Sol\'e, Pastor-Satorras et al. in which the graph grows according to a…

Lua (Ierusalimschy et al., 1996) is a well-known scripting language, popular among many programmers, most notably in the gaming industry. Remarkably, the only data-structuring mechanism in Lua are associative arrays, called tables. With Lua…

Horizontal gene transfer inference approaches are usually based on gene sequences: parametric methods search for patterns that deviate from a particular genomic signature, while phylogenetic methods use sequences to reconstruct the gene and…

Minimum resolution set and associated metric dimension provide the basis for unique and systematic labeling of nodes of a graph using distances to a set of landmarks. Such a distance vector set, however, may not be unique to the graph and…

Evaluating the reliability of complex technical networks, such as those in energy distribution, logistics, and transportation systems, is of paramount importance. These networks are often represented as multistate flow networks (MFNs).…

Although the expenses associated with DNA sequencing have been rapidly decreasing, the current cost of sequencing information stands at roughly $120/GB, which is dramatically more expensive than reading from existing archival storage…

Randomized rumor spreading processes diffuse information on an undirected graph and have been widely studied. In this work, we present a generic framework for analyzing a broad class of such processes on regular graphs. Our analysis is…

This paper introduces the \emph{$d$-distance $b$-matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges, an integer $d\in\mathbb{Z}_+$ and a degree bound function…

Discrete-value time series are sequences of measurements where each measurement is a discrete (categorical or integer) value. These time series are widely used in various fields, and their classification and clustering are essential for…

The longest induced (or chordless) cycle problem is a graph problem classified as NP-complete and involves the task of determining the largest possible subset of vertices within a graph in such a way that the induced subgraph forms a cycle.…

For an angle $\alpha\in (0,\pi)$, we consider plane graphs and multigraphs in which the edges are either (i) one-bend polylines with an angle $\alpha$ between the two edge segments, or (ii) circular arcs of central angle $2(\pi-\alpha)$. We…

This paper addresses the optimal design of wireless networks through the site and power assignment problem. Given a set of candidate transmitters, this problem involves choosing optimal transmitter locations and powers to provide service…

Since the seminal result of Karger, Motwani, and Sudan, algorithms for approximate 3-coloring have primarily centered around SDP-based rounding. However, it is likely that important combinatorial or algebraic insights are needed in order to…

The problems of determining the permutation-representation number (prn) and the representation number of bipartite graphs are open in the literature. Moreover, the decision problem corresponding to the determination of the prn of a…

In the recently introduced framework of solution discovery via reconfiguration [Fellows et al., ECAI 2023], we are given an initial configuration of $k$ tokens on a graph and the question is whether we can transform this configuration into…

In this article, we consider several models of random walks in one or several dimensions, additionally allowing, at any unit of time, a reset (or "catastrophe") of the walk with probability $q$. We establish the distribution of the final…

This case-study aims at a comparison of the service quality of time-tabled buses as compared to on-demand ridepooling cabs in the late evening hours in the city of Wuppertal, Germany. To evaluate the service quality of ridepooling as…