离散数学

Using the algebraic approach to promise constraint satisfaction problems, we establish complexity classifications of three natural variants of hypergraph colourings: standard nonmonochromatic colourings, conflict-free colourings, and…

We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…

Many familial diseases are caused by genetic accidents, which affect both the genome and its epigenetic environment, expressed as an interaction graph between the genes as that involved in one familial disease we shall study, the hereditary…

There are numerous randomized algorithms to generate spanning trees in a given ambient graph; several target the uniform distribution on trees (UST), while in practice the fastest and most frequently used draw random weights on the edges…

Temporal graphs are graphs whose edges are labelled with times at which they are active. Their time-sensitivity provides a useful model of real networks, but renders many problems studied on temporal graphs more computationally complex than…

Staff scheduling is a well-known problem in operations research and finds its application at hospitals, airports, supermarkets, and many others. Its goal is to assign shifts to staff members such that a certain objective function, e.g.…

We study the problem of enumerating Tarski fixed points on finite lattices. We derive query complexity lower bounds for finding three or more Tarski fixed points of isotone maps and the subclasses of increasing and decreasing isotone maps.…

We present a formal proof of the Sands-Sauer-Woodrow (SSW) theorem using the Rocq proof assistant and the MathComp/SSReflect library. The SSW theorem states that in a directed graph whose edges are colored with two colors and that contains…

Given an edge-colored graph, the Maximum Rainbow Matching problem asks for a maximum-cardinality matching of the graph that contains at most one edge from each color. We provide the following complexity dichotomy for this problem based on…

Conjunctive normal forms where every clause has length at most two are called 2-CNFs. We study minimally unsatisfiable 2-CNFs (2-MUs), that is, unsatisfiable 2-CNFs where removing any clause destroys unsatisfiability, and obtain their full…

Spanning trees are fundamental for efficient communication in networks. For fault-tolerant communication, it is desirable to have multiple spanning trees to ensure resilience against failures of nodes and edges. To this end, various notions…

A function $\varphi:\{0,1\}^n \to \{0,1\}^N$ is called an isometric embedding of the $n$-dimensional Hamming metric space to the $N$-dimensional edit metric space if, for all $x,y\in\{0,1\}^n$, the Hamming distance between $x$ and $y$ is…

In this paper, we investigate the relationships between the volumes of four convex bodies: the cut polytope, metric polytope, rooted metric polytope, and elliptope, defined on graphs with $n$ vertices. The cut polytope is contained in each…

The problem of finding the general classification of geodetic graphs is still open. We believe that one of the obstacles to attain this goal is that geodetic graphs lack a structural description. In other words, their fundamental properties…

A temporal graph is a graph whose edges appear at certain points in time. These graphs are temporally connected (in class TC) if all vertices can reach each other by temporal paths (traversing the edges in chronological order). Reachability…

Let $G = V, E$ be a simple connected undirected graph. A set $X \subseteq V$ is \emph{geodesically convex} if for any pair of vertices $x, y \in X$, all vertices on all shortest paths in $G$ from $x$ to $y$ are contained in $X$. A set $H…

Much work has been devoted to bent functions in odd characteristic, but there still remains a gap between our knowledge of binary and nonbinary bent functions. In the first part of this paper, we attempt to partially bridge this gap by…

For a graph $ G = (V, E) $ with a vertex set $ V $ and an edge set $ E $, a function $ f : V \rightarrow \{0, 1, 2, . . . , diam(G)\} $ is called a \emph{broadcast} on $ G $. For each vertex $ u \in V $, if there exists a vertex $ v $ in $…

A $k$-edge-weighting of $G$ is a mapping $\omega:E(G)\longrightarrow \{1,\ldots,k\}$. The edge-weighting of $G$ naturally induces a vertex-colouring $\sigma_{\omega}:V(G)\longrightarrow \mathbb{N}$ given by$\sigma_{\omega}(v)=\sum_{u\in…

We introduce a variant of the vertex-distinguishing edge coloring problem, where each edge is assigned a subset of colors. The label of a vertex is the union of the sets of colors on edges incident to it. In this paper we investigate the…