Rémi Watrigant
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View article: Subcoloring of (Unit) Disk Graphs
Subcoloring of (Unit) Disk Graphs Open
A subcoloring of a graph is a partition of its vertex set into subsets (called colors), each inducing a disjoint union of cliques. It is a natural generalization of the classical proper coloring, in which each color must instead induce an …
View article: Identifying hard native instances for the maximum independent set problem on neutral atoms quantum processors
Identifying hard native instances for the maximum independent set problem on neutral atoms quantum processors Open
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world …
View article: Twin-Width III: Max Independent Set, Min Dominating Set, and Coloring
Twin-Width III: Max Independent Set, Min Dominating Set, and Coloring Open
We recently introduced the graph invariant twin-width, and showed that first-order model checking can be solved in time $f(d,k)n$ for $n$-vertex graphs given with a witness that the twin-width is at most $d$, called $d$-contraction sequenc…
View article: A structural description of Zykov and Blanche Descartes graphs
A structural description of Zykov and Blanche Descartes graphs Open
In 1949, Zykov proposed the first explicit construction of triangle-free graphs with arbitrarily large chromatic number. We define a Zykov graph as any induced subgraph of a graph created using Zykov's construction. We give a structural ch…
View article: Channel allocation revisited through 1-extendability of graphs
Channel allocation revisited through 1-extendability of graphs Open
We revisit the classical problem of channel allocation for Wi-Fi access points (AP). Using mechanisms such as the CSMA/CA protocol, Wi-Fi access points which are in conflict within a same channel are still able to communicate to terminals.…
View article: Beyond recognizing well-covered graphs
Beyond recognizing well-covered graphs Open
We prove a number of results related to the computational complexity of recognizing well-covered graphs. Let $k$ and $s$ be positive integers and let $G$ be a graph. Then $G$ is said - $\mathbf{W_k}$ if for any $k$ pairwise disjoint indepe…
View article: On the Limits of Information Spread by Memory-Less Agents
On the Limits of Information Spread by Memory-Less Agents Open
We address the self-stabilizing bit-dissemination problem, designed to capture the challenges of spreading information and reaching consensus among entities with minimal cognitive and communication capacities. Specifically, a group of n ag…
View article: 1-extendability of independent sets
1-extendability of independent sets Open
In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational c…
View article: Approximating Highly Inapproximable Problems on Graphs of Bounded Twin-Width
Approximating Highly Inapproximable Problems on Graphs of Bounded Twin-Width Open
For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximatio…
View article: Twin-width II: small classes
Twin-width II: small classes Open
The recently introduced twin-width of a graph G is the minimum integer d suchthat G has a d-contraction sequence, that is, a sequence of |V (G)|− 1 iterated vertex identifications for which the overall maximum number of red edges incident …
View article: 1-Extendability of independent sets
1-Extendability of independent sets Open
In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational c…
View article: Twin-width and polynomial kernels
Twin-width and polynomial kernels Open
We study the existence of polynomial kernels, for parameterized problems without a polynomial kernel on general graphs, when restricted to graphs of bounded twin-width. Our main result is that a polynomial kernel for $k$-Dominating Set on …
View article: First-Order Transductions of Graphs (Invited Talk)
First-Order Transductions of Graphs (Invited Talk) Open
This paper is an extended abstract of my STACS 2021 talk "First-order transductions of graphs".
View article: Twin-width I: tractable FO model checking
Twin-width I: tractable FO model checking Open
Inspired by a width invariant defined on permutations by Guillemot and Marx [SODA’14], we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, K t -free unit d -d…
View article: Twin-width II: small classes
Twin-width II: small classes Open
The twin-width of a graph $G$ is the minimum integer $d$ such that $G$ has a $d$-contraction sequence, that is, a sequence of $|V(G)|-1$ iterated vertex identifications for which the overall maximum number of red edges incident to a single…
View article: An algorithmic weakening of the Erd\H{o}s-Hajnal conjecture
An algorithmic weakening of the Erd\H{o}s-Hajnal conjecture Open
We study the approximability of the Maximum Independent Set (MIS) problem in\n$H$-free graphs (that is, graphs which do not admit $H$ as an induced\nsubgraph). As one motivation we investigate the following conjecture: for every\nfixed gra…
View article: An algorithmic weakening of the Erdős-Hajnal conjecture
An algorithmic weakening of the Erdős-Hajnal conjecture Open
We study the approximability of the Maximum Independent Set (MIS) problem in $H$-free graphs (that is, graphs which do not admit $H$ as an induced subgraph). As one motivation we investigate the following conjecture: for every fixed graph …
View article: Comparing Two Clusterings Using Matchings between Clusters of Clusters
Comparing Two Clusterings Using Matchings between Clusters of Clusters Open
Clustering is a fundamental problem in data science, yet the variety of clustering methods and their sensitivity to parameters make clustering hard. To analyze the stability of a given clustering algorithm while varying its parameters, and…
View article: When Maximum Stable Set can be solved in FPT time
When Maximum Stable Set can be solved in FPT time Open
Maximum Independent Set (MIS for short) is in general graphs the paradigmatic $W[1]$-hard problem. In stark contrast, polynomial-time algorithms are known when the inputs are restricted to structured graph classes such as, for instance, pe…
View article: Constraint Generation Algorithm for the Minimum Connectivity Inference\n Problem
Constraint Generation Algorithm for the Minimum Connectivity Inference\n Problem Open
Given a hypergraph $H$, the Minimum Connectivity Inference problem asks for a\ngraph on the same vertex set as $H$ with the minimum number of edges such that\nthe subgraph induced by every hyperedge of $H$ is connected. This problem has\nr…
View article: Overlaying a hypergraph with a graph with bounded maximum degree
Overlaying a hypergraph with a graph with bounded maximum degree Open
International audience
View article: Parameterized Complexity of Independent Set in H-Free Graphs
Parameterized Complexity of Independent Set in H-Free Graphs Open
In this paper, we investigate the complexity of Maximum Independent Set (MIS) in the class of H-free graphs, that is, graphs excluding a fixed graph as an induced subgraph. Given that the problem remains NP-hard for most graphs H, we study…
View article: Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq
Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq Open
We describe a procedure to derive equality tests and their correctness proofs from inductive type declarations in Coq. Programs and proofs are derived compositionally, reusing code and proofs derived previously. The key steps are two. Firs…