离散数学
In the BFA 2023 conference paper, A. Polujan, L. Mariot and S. Picek exhibited the first example of a non-normal but weakly normal bent function in dimension 8. In this note, we present numerical approaches based on the classification of…
We obtain the smallest unsatisfiable formulas in subclasses of $k$-CNF (exactly $k$ distinct literals per clause) with bounded variable or literal occurrences. Smaller unsatisfiable formulas of this type translate into stronger…
The Storage Location Assignment Problem (SLAP) and the Picker Routing Problem (PRP) have received significant attention in the literature due to their pivotal role in the performance of the Order Picking (OP) activity, the most…
High dimensional expanders (HDXs) are a hypergraph generalization of expander graphs. They are extensively studied in the math and TCS communities due to their many applications. Like expander graphs, HDXs are especially interesting for…
Dominating sets in graphs are often used to model some monitoring of the graph: guards are posted on the vertices of the dominating set, and they can thus react to attacks occurring on the unguarded vertices by moving there (yielding a new…
Given a graph $G(V,E)$, a vertex subset $S$ of $G$ is called an open packing in $G$ if no pair of distinct vertices in $S$ have a common neighbour in $G$. The size of a largest open packing in $G$ is called the open packing number,…
A module of a graph G is a set of vertices that have the same set of neighbours outside. Modules of a graphs form a so-called partitive family and thereby can be represented by a unique tree MD(G), called the modular decomposition tree.…
One of the open problems in machine learning is whether any set-family of VC-dimension $d$ admits a sample compression scheme of size $O(d)$. In this paper, we study this problem for balls in graphs. For a ball $B=B_r(x)$ of a graph…
A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that…
An orientable sequence of order $n$ over an alphabet $\{0,1,\ldots, k{-}1\}$ is a cyclic sequence such that each length-$n$ substring appears at most once \emph{in either direction}. When $k= 2$, efficient algorithms are known to construct…
In this study, we investigate the problem of comparing gene trees reconciled with the same species tree using a novel semi-metric, called the Path-Label Reconciliation (PLR) dissimilarity measure. This approach not only quantifies…
We present a convenient trick for computing the sizes of clusters within a network. The rationale relies on the mathematics of the geometric series and the fundamental matrix of a Markov Chain.
We address the convergence rate of Markov chains for randomly generating an edge coloring of a given tree. Our focus is on the Glauber dynamics which updates the color at a randomly chosen edge in each step. For a tree $T$ with $n$ vertices…
Consider a graph $G = (V, E)$ and a function $f: V \rightarrow \{0, 1, 2\}$. A vertex $u$ with $f(u)=0$ is defined as \emph{undefended} by $f$ if it lacks adjacency to any vertex with a positive $f$-value. The function $f$ is said to be a…
A subset of vertices in a graph is called resolving when the geodesic distances to those vertices uniquely distinguish every vertex in the graph. Here, we characterize the resolvability of Hamming graphs in terms of a constrained linear…
Efficiently enumerating all the extreme points of a polytope identified by a system of linear inequalities is a well-known challenge issue.We consider a special case and present an algorithm that enumerates all the extreme points of a…
Many standard graph classes are known to be characterized by means of layouts (a permutation of its vertices) excluding some patterns. Important such graph classes are among others: proper interval graphs, interval graphs, chordal graphs,…
Closeness is one of the most studied characteristics of networks. Residual closeness is a very sensitive measure of graphs robustness. Additional closeness is a measure of growth potentials of networks. In this article we calculate the…
We present several advancements in search-type problems for fleets of mobile agents operating in two dimensions under the wireless model. Potential hidden target locations are equidistant from a central point, forming either a disk…
We consider \emph{weighted group search on a disk}, which is a search-type problem involving 2 mobile agents with unit-speed. The two agents start collocated and their goal is to reach a (hidden) target at an unknown location and a known…