Concept

Théorème des quatre couleurs

Publications associées (20)

Recoloring subgraphs of K-2n for sports scheduling

The exploration of one-factorizations of complete graphs is the foundation of some classical sports scheduling problems. One has to traverse the landscape of such one-factorizations by moving from one of those to a so-called neighbor one-factorization. Thi ...

ELSEVIER2021

Minimal graphs for 2-factor extension

Dominique de Werra

Let G = (V, E) be a simple loopless finite undirected graph. We say that G is (2-factor) expandable if for any non-edge uv, G + uv has a 2-factor F that contains uv. We are interested in the following: Given a positive integer n = vertical bar V vertical b ...

ELSEVIER2020

Distributed Coloring of Graphs with an Optimal Number of Colors

Etienne Michel François Bamas

This paper studies sufficient conditions to obtain efficient distributed algorithms coloring graphs optimally (i.e. with the minimum number of colors) in the LOCAL model of computation. Most of the work on distributed vertex coloring so far has focused on ...

SCHLOSS DAGSTUHL, LEIBNIZ CENTER INFORMATICS2019

Form finding in elastic gridshells

Pedro Miguel Nunes Pereira de Almeida Reis, Changyeob Baek

Elastic gridshells comprise an initially planar network of elastic rods that are actuated into a shell-like structure by loading their extremities. The resulting actuated form derives from the elastic buckling of the rods subjected to inextensibility. We s ...

National Academy of Sciences2018

Combinatorics of Loop Equations for Branched Covers of Sphere

Nicolas Gerson Orantin

We prove, in a purely combinatorial way, the spectral curve topological recursion for the problem of enumeration of bi-colored maps, which are dual objects to dessins d'enfant. Furthermore, we give a proof of the quantum spectral curve equation for this pr ...

OXFORD UNIV PRESS2018

Unsplittable coverings in the plane

János Pach, Doemoetoer Palvoelgyi

A system of sets forms an m-fold covering of a set X if every point of X belongs to at least m of its members. A 1-fold covering is called a covering. The problem of splitting multiple coverings into several coverings was motivated by classical density est ...

Academic Press Inc Elsevier Science2016

Unsplittable Coverings in the Plane

János Pach, Doemoetoer Palvoelgyi

Springer-Verlag Berlin2016

Well-Posedness, Regularity, and Convergence Analysis of the Finite Element Approximation of a Generalized Robin Boundary Value Problem

Alfio Quarteroni, Luca Dede', Claudia Maria Colciago

In this paper, we propose the mathematical and finite element analysis of a second-order partial differential equation endowed with a generalized Robin boundary condition which involves the Laplace--Beltrami operator by introducing a function space $H^1(\O ...

Society for Industrial and Applied Mathematics2015

Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

Bartosz Maria Walczak, Michal Lason

Several classical constructions illustrate the fact that the chromatic number of a graph may be arbitrarily large compared to its clique number. However, until very recently no such construction was known for intersection graphs of geometric objects in the ...

Springer US2013

On the Performance of Percolation Graph Matching

Matthias Grossglauser, Lyudmila Yartseva

Graph matching is a generalization of the classic graph isomorphism problem. By using only their structures a graph-matching algorithm finds a map between the vertex sets of two similar graphs. This has applications in the de-anonymization of social and in ...

ACM2013

On Zero-Dimensional Exciton-Polaritons

Roland Cerna

Microcavity exciton-polaritons are half-matter half-light quasiparticles with outstanding properties. This offers a great way to access and control fundamental excitations in a solid by simple optical means. Therefore, apart from their importance in fundam ...

EPFL2011

Split-critical and uniquely split-colorable graphs

Dominique de Werra, Bernard Ries, Tinaz Ekim

The split-coloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring p ...

2010

Optimistic chordal coloring: a coalescing heuristic for SSA form programs

Paolo Ienne, Philip Brisk, Ajay Kumar Verma

The interference graph for a procedure in Static Single Assignment (SSA) Form is chordal. Since the k-colorability problem can be solved in polynomial-time for chordal graphs, this result has generated interest in SSA-based heuristics for spilling and coal ...

Springer US2009

A tutorial on the use of graph coloring for some problems in robotics

Dominique de Werra, Tinaz Ekim

We study the problem where a robot has to pick up items of different sizes which are stored along a corridor. A natural requirement is that the items have to be collected in decreasing order of their sizes. We deal with various systems according to the loc ...

2009

Graph colouring approaches for a satellite range scheduling problem

Nicolas Zufferey, Patrick Amstutz, Philippe Giaccari

A goal of this paper is to efficiently adapt the best ingredients of the graph colouring techniques to an NP-hard satellite range scheduling problem, called MuRRSP. We propose two new heuristics for the MuRRSP, where as many jobs as possible have to be sch ...

2008

On the essential dimension of cyclic p-groups

Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r >= 1 be an integer. We compute the essential dimension of Z/p(r) Z over K (Theorem 4.1). In particular, i) We have edℚ(ℤ/8ℤ)=4, a result which ...

Springer-Verlag2008

A graph coloring heuristic using partial solutions and a reactive tabu scheme

Nicolas Zufferey

Most of the recent heuristics for the graph coloring problem start from an infeasible k-coloring (adjacent vertices may have the same color) and try to make the solution feasible through a sequence of color exchanges. In contrast, our approach (called FOO- ...

2008

Variations of coloring problems related to scheduling and discrete tomography

Bernard Ries

The graph coloring problem is one of the most famous problems in graph theory and has a large range of applications. It consists in coloring the vertices of an undirected graph with a given number of colors such that two adjacent vertices get different col ...

EPFL2007

Generalized vertex coloring problems using split graphs

Tinaz Ekim

Graph theory experienced a remarkable increase of interest among the scientific community during the last decades. The vertex coloring problem (Min Coloring) deserves a particular attention rince it has been able to capture a wide variety of applications. ...

EPFL2006

Partitioning cographs into cliques and stable sets

Dominique de Werra, Tinaz Ekim

We consider the problem of partitioning the node set of a graph into p cliques and k stable sets, namely the (p,k)-coloring problem. Results have been obtained for general graphs \cite{hellcomp}, chordal graphs \cite{hellchordal} and cacti for the case whe ...

2005