离散数学

In balanced allocations, the goal is to place $m$ balls into $n$ bins, so as to minimize the gap (difference of max to average load). The One-Choice process places each ball to a bin sampled independently and uniformly at random. The…

In multi-objective optimization, several potentially conflicting objective functions need to be optimized. Instead of one optimal solution, we look for the set of so called non-dominated solutions. An important subset is the set of…

When we focus on finite dynamical systems from both the computability/complexity and the modelling standpoints, automata networks seem to be a particularly appropriate mathematical model on which theory shall be developed. In this paper,…

This work formalizes efficient Fast Fourier-based multiplication algorithms for polynomials in quotient rings such as $\mathbb{Z}_{m}[x]/\left<x^{n}-a\right>$, with $n$ a power of 2 and $m$ a non necessarily prime integer. We also present a…

This preprint makes the claim of having computed the $9^{th}$ Dedekind Number. This was done by building an efficient FPGA Accelerator for the core operation of the process, and parallelizing it on the Noctua 2 Supercluster at Paderborn…

The notion of $12$-representable graphs was introduced as a variant of a well-known class of word-representable graphs. Recently, these graphs were shown to be equivalent to the complements of simple-triangle graphs. This indicates that a…

We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.

We formulate and study a two-player static duel game as a nonzero-sum discounted stochastic game. Players $P_{1},P_{2}$ are standing in place and, in each turn, one or both may shoot at the other player. If $P_{n}$ shoots at $P_{m}$ ($m\neq…

The Walsh--Hadamard spectrum of a bent function uniquely determines a dual function. The dual of a bent function is also bent. A bent function that is equal to its dual is called a self-dual function. The Hamming distance between a bent…

We study vulnerability of a uniformly distributed random graph to an attack by an adversary who aims for a global change of the distribution while being able to make only a local change in the graph. We call a graph property $A$…

A retrospective fleet-sizing problem can be solved via bipartite matching, where a maximum cardinality matching corresponds to the minimum number of vehicles needed to cover all trips. We prove a min-max theorem on this minimum fleet-size…

The class of (eventually) dendric words generalizes well-known families such as the Arnoux-Rauzy words or the codings of interval exchanges. There are still many open questions about the link between dendricity and morphisms. In this paper,…

A graph is circle if its vertices are in correspondence with a family of chords in a circle in such a way that every two distinct vertices are adjacent if and only if the corresponding chords have nonempty intersection. Even though there…

Interval and proper interval graphs are very well-known graph classes, for which there is a wide literature. As a consequence, some generalizations of interval graphs have been proposed, in which graphs in general are expressed in terms of…

The thinness of a graph is a width parameter that generalizes some properties of interval graphs, which are exactly the graphs of thinness one. Many NP-complete problems can be solved in polynomial time for graphs with bounded thinness,…

By providing a new framework, we extend previous results on locally checkable problems in bounded treewidth graphs. As a consequence, we show how to solve, in polynomial time for bounded treewidth graphs, double Roman domination and Grundy…

A contact $B_0$-VPG graph is a graph for which there exists a collection of nontrivial pairwise interiorly disjoint horizontal and vertical segments in one-to-one correspondence with its vertex set such that two vertices are adjacent if and…

Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study…

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the…

For real $\alpha\in [0,1)$ and a hypergraph $G$, the $\alpha$-spectral radius of $G$ is the largest eigenvalue of the matrix $A_{\alpha}(G)=\alpha D(G)+(1-\alpha)A(G)$, where $A(G)$ is the adjacency matrix of $G$, which is a symmetric…