离散数学

We consider the mixed search game against an agile and visible fugitive. This is the variant of the classic fugitive search game on graphs where searchers may be placed to (or removed from) the vertices or slide along edges. Moreover, the…

In a strongly connected graph $G = (V,E)$, a cut arc (also called strong bridge) is an arc $e \in E$ whose removal makes the graph no longer strongly connected. Equivalently, there exist $u,v \in V$, such that all $u$-$v$ walks contain $e$.…

The traditional complex network approach considers only the shortest paths from one node to another, not taking into account several other possible paths. This limitation is significant, for example, in urban mobility studies. In this short…

We present a new flow-based formulation for identical parallel machine scheduling with a regular objective function and without idle time. The formulation is constructed with the help of a decision diagram that represents all job sequences…

In a random intersection graph $G_{n,m,p}$, each of $n$ vertices selects a random subset of a set of $m$ labels by including each label independently with probability $p$ and edges are drawn between vertices that have at least one label in…

In this paper, we study a class of discrete Morse functions, coming from Discrete Morse Theory, that are equivalent to a class of simplicial stacks, coming from Mathematical Morphology. We show that, as in Discrete Morse Theory, we can see…

We introduce a supporting combinatorial framework for the Flat Wall Theorem. In particular, we suggest two variants of the theorem and we introduce a new, more versatile, concept of wall homogeneity as well as the notion of regularity in…

We consider classes of objective functions of cardinality constrained maximization problems for which the greedy algorithm guarantees a constant approximation. We propose the new class of $\gamma$-$\alpha$-augmentable functions and prove…

Given $n$ subspaces of a finite-dimensional vector space over a fixed finite field $\mathbb F$, we wish to find a "branch-decomposition" of these subspaces of width at most $k$ that is a subcubic tree $T$ with $n$ leaves mapped bijectively…

In this paper we count set closure systems (also known as Moore families) for the case when all single element sets are closed. In particular, we give the numbers of such strict (empty set included) and non-strict families for the base set…

We investigate pruning in search trees of so-called quantified integer linear programs (QIPs). QIPs consist of a set of linear inequalities and a minimax objective function, where some variables are existentially and others are universally…

The input to the \emph{Triangle Evacuation} problem is a triangle $ABC$. Given a starting point $S$ on the perimeter of the triangle, a feasible solution to the problem consists of two unit-speed trajectories of mobile agents that…

We study two modifications of the Post Correspondence Problem (PCP), namely 1) the bi-infinite version, where it is asked whether there exists a bi-infinite word such that two given morphisms agree on it, and 2) the conjugate version, where…

We study a patrolling game played on a network $Q$, considered as a metric space. The Attacker chooses a point of $Q$ (not necessarily a node) to attack during a chosen time interval of fixed duration. The Patroller chooses a unit speed…

We initiate the study of Ramsey numbers of trails. Let $k \geq 2$ be a positive integer. The Ramsey number of trails with $k$ vertices is defined as the the smallest number $n$ such that for every graph $H$ with $n$ vertices, $H$ or the…

In the eternal vertex cover problem, mobile guards on the vertices of a graph are used to defend it against an infinite sequence of attacks on its edges by moving to neighbor vertices. The eternal vertex cover problem consists in…

Teaching graph theory with the most adequate tools requires time and ideas. We present how an open community of teachers shares contents and ideas on an innovative platform. The objective is to get the students autonomous in their training…

We look at constructions of aperiodic SFTs on fundamental groups of graph of groups. In particular we prove that all generalized Baumslag-Solitar groups (GBS) admit a strongly aperiodic SFT. Our proof is based on a structural theorem by…

We present the different distances on tilings of Rd that exist in the literature, we prove that (most of) these definitions are correct (i.e. they indeed define metrics on tilings of Rd ). We prove that for subshifts with finite local…

Given a collection of red and blue mobile agents located on two grid rows, we seek to move all the blue agents to the far left side and all the red agents to the far right side, thus \textit{physically sorting} them according to color. The…